Absolute Value

Problem 1

Намерете корена на уравнението $|3^{2}-2^{4}|-x=|5 \frac{1}{3}-5 \frac{5}{6}|$ . Изберете от A) $-7 \frac{1}{6}$ , Б) $-6 \frac{5}{6}$ , B) $6 \frac{1}{2}$ , Г) $7 \frac{1}{6}$ .

See Solution

Problem 2

Намери $x$ от уравнението $\left|3^{2}-2^{4}\right|-x=\left|5 \frac{1}{3}-5 \frac{5}{6}\right|$ .

See Solution

Problem 3

If $|x-3|>5$ , which inequalities are true? a) $-2<x<8$ b) $-8<x<2$ c) $x<-8 \cup x>2$ d) $x<-2 \cup x>8$ e) $x<-8 \cup x>-2$

See Solution

Problem 4

Graph $g(x)=|x-2|$ and compare it to $f(x)=|x|$ . Describe the domain and range. Select the correct translation and range.

See Solution

Problem 5

Graph $g(x)=-\frac{1}{4}|x|$ . Compare to $f(x)=|x|$ and describe domain and range. Choose the correct option.

See Solution

Problem 6

Describe the transformations from $f(x)=|x|$ to $g(x)=2|x+1|-2$ and graph $g(x)$ . Choose the correct transformation option.

See Solution

Problem 7

Identify the transformations from $f(x)=|x|$ to $g(x)=-|x+2|+3$ and choose the correct description.

See Solution

Problem 8

Jonael dropped a sandbag from a balloon 250 meters above a target. The bag is 75 meters below the balloon. Find 2 expressions for the distance to the target. Choose 2 answers: A $|-250+75|$ B $|-75+250|$ C $|250+75|$

See Solution

Problem 9

Find $x$ such that $\sqrt{18-x}-\sqrt{2x}=\sqrt{x+2}$ and $\left|\frac{x+1}{x-4}\right|<3$ .

See Solution

Problem 10

Is the statement true or false: $19.7 < |19.7|$ ? Answer: True O False

See Solution

Problem 11

Find the number of solutions for the equation $|x|=75$ . Options: No Solution, One Solution, Two Solutions.

See Solution

Problem 12

Solve the equation $|x| = -16$ . What is the solution set?

See Solution

Problem 13

Find the range of the function $f(x)=|x|-3$ . Options include $f(x) \geq -3$ , $f(x) < -3$ , $f(x) \leq -3$ , $f(x) > -3$ .

See Solution

Problem 14

Solve the inequality $|x-3| \leq 5$ .

See Solution

Problem 15

Determine the domain, range, intervals of increase/decrease, x-intercepts, and y-intercept for $f(x)=2|x+3|-6$ .

See Solution

Problem 16

Identify the absolute value parent function from the options: A. $f(x)=|2 x|$ , B. $f(x)=|x|$ , C. $f(x)=|x|-2$ , D. $f(x)=|x|+1$ .

See Solution

Problem 17

Find the domain and range of the absolute value function: A. $y<0$ , B. all reals, $y \geq 0$ , C. $y \geq 0$ , D. all reals, $y>0$ .

See Solution

Problem 18

Identify the equation that represents an absolute value function from these options: $f(x)=-9$ , $f(x)=\frac{1}{3 x}$ , $f(x)=x-3 x^{2}$ , $f(x)=\frac{-1}{4}|x+4|-3$ .

See Solution

Problem 19

Analyze the function $f(x)=|x-3|-1$ : find domain, range, intercepts, increasing/decreasing intervals, and end behavior.

See Solution

Problem 20

Solve the equation $-7|3-6 x|-4=-67$ .

See Solution

Problem 21

Solve the equation $\frac{|-9+2 p|}{4}=2$ .

See Solution

Problem 22

Solve for $x$ in the equation $9 + |7 + 5x| = 61$ .

See Solution

Problem 23

Solve the equation $1 - 8|-5x + 9| = 9$ .

See Solution

Problem 24

Solve the equation $-8|-5 x+9|=9$ .

See Solution

Problem 25

Evaluate $-4|5+m|$ for $m=-3$ . What is the result?

See Solution

Problem 26

Identify the parent function and transformations for: $y=2|x+4|+4$ .

See Solution

Problem 27

Graph $f(x)=\frac{|x+2|}{x+2}$ for the range $[-4,4]$ .

See Solution

Problem 28

Solve for $n$ in the equation $3|2-5n|=0$ .

See Solution

Problem 29

Define the absolute value function $f(x)=|4x+7|$ as a piecewise function.

See Solution

Problem 30

Solve the equation $\frac{|5 x+5|}{-5}=-10$ .

See Solution

Problem 31

Solve the equation: $\frac{|x+13|}{-2}=-20$ .

See Solution

Problem 32

Solve for $x$ : $\frac{-|2 x+2|}{5}=-10$

See Solution

Problem 33

Daniel spends around \$30 on gas at \$2.50 per gallon. Write an inequality to find the range of gallons he can buy.

See Solution

Problem 34

Solve the equation $|5 y-4|=7$ .

See Solution

Problem 35

Simplify the expression $\frac{15-z}{|15-z|}$ for the case when $z<15$ .

See Solution

Problem 36

Solve $10|7 x+7|+10 \geq 80$ for $x$ .

See Solution

Problem 37

Find $f(6+h)$ for $f(x)=\frac{|x-6|}{x-6}$ when $h<0$ .

See Solution

Problem 38

Solve the inequality $|9 n + 2| + 9 \geq 47$ .

See Solution

Problem 39

Find the min and max lengths for nails allowed to vary by $\frac{1}{32}$ inch from 1 inch. Is a 1.05 inch nail acceptable?

See Solution

Problem 40

Evaluate $|6x + 4y|$ for $x = 4$ and $y = -1$ .

See Solution

Problem 41

Solve the inequality: $10|7x + 7| + 10 \geq 80$ .

See Solution

Problem 42

Evaluate $|f-71|$ for $f=-4$ .

See Solution

Problem 43

Evaluate $32|r|-7$ for $r=-2$ .

See Solution

Problem 44

Evaluate $q + 9|p|$ for $p=2$ and $q=-66$ .

See Solution

Problem 45

Evaluate $m + 62|k|$ for $k = -1$ and $m = -59$ .

See Solution

Problem 46

Evaluate $-4|w| + 630$ for $w = 83$ .

See Solution

Problem 47

Solve the inequality $9|2 x-1|+4<49$ .

See Solution

Problem 48

Find the graph of the inequality $|\frac{1}{2} x + 2| \geq 1$ .

See Solution

Problem 49

Graph the inequality $\left|\frac{1}{2} x + 2\right| \geq 1$ .

See Solution

Problem 50

Solve the equation $|3 x+5|=5 x+2$ . What are the possible values of $x$ ?

See Solution

Problem 51

Solve: $8|3x-5|=56$ . Choose the correct solution set from: a. $\{-4\}$ b. $\left\{-4, \frac{2}{3}\right\}$ c. $\left\{-\frac{2}{3}, 4\right\}$ d. $\left\{4,-\frac{14}{3}\right\}$ .

See Solution

Problem 52

Solve the inequality $|x-7|+12 \leq 25$ and select the correct solution set from the options given.

See Solution

Problem 53

Identify the equation of the vertically stretched and shifted absolute value function: 3 left, 8 down. Options: a. $f(x)=2|x+3|-8$ b. $f(x)=\frac{1}{2}|x+3|-8$ c. $f(x)=2|x=3|-8$ d. $f(x)=\frac{1}{2}|x-3|-8$

See Solution

Problem 54

Solve the equation: $\left|\frac{5}{x-3}\right|=15$

See Solution

Problem 55

Graph the piecewise function $p(x)$ defined as:
$p(x) = -2|x+6| + 7$ for $-8 \leq x < -3$ , $\frac{1}{3} x - 2$ for $-3 < x \leq 3$ , and $(x-5)^{2} - 5$ for $3 < x < 8$ .

See Solution

Problem 56

Calculate $|2y-5|$ when $y = 5$ .

See Solution

Problem 57

Solve for $z$ in the equation $7 - |3z + 10| = 0$ .

See Solution

Problem 58

Calculate the expression $-|2(1.2)-4|$ .

See Solution

Problem 59

Solve the equation $|x-3|=17$ .

See Solution

Problem 60

Evaluate $3|x+4|+|3x|$ for $x = -4$ .

See Solution

Problem 61

Solve the equation: $|x-3|=17$ .

See Solution

Problem 62

Solve the equation $8|x-3|=88$ .

See Solution

Problem 63

Solve the equation $|12+4 x|=16$ .

See Solution

Problem 64

Solve the equation $|3 x-10|=17$ .

See Solution

Problem 65

Graph the inequality $|4x + 2| < 10$ .

See Solution

Problem 66

Solve $|5 x|=70$ . What are the possible values of $x$ ?

See Solution

Problem 67

Find the vertex of the function $f(x)=|x-4|+3$ . What are the coordinates of the vertex?

See Solution

Problem 68

Find the domain and range of the function $f(x)=|x-4|+3$ .

See Solution

Problem 69

Find the function $g(x)$ that reflects $f(x)=|6x|-2$ in the $y$ -axis.

See Solution

Problem 70

Solve the inequality $|x-1|-2x>1$ .

See Solution

Problem 71

Find the value of $f(8)$ for the function $f(x)=|x-3|-5$ .

See Solution

Problem 72

Solve for $x$ : $2|3 x-4|+15=43$

See Solution

Problem 73

Graph the equation $y=-5|x|$ and describe its transformation from $f(x)=|x|$ . Choose the correct graph.

See Solution

Problem 74

Graph the equation $y=-5|x|$ and describe the transformation from $f(x)=|x|$ . Choose the correct option.

See Solution

Problem 75

Find the max and min diameters of bolts with a target of $6.5 \mathrm{~mm}$ and tolerance of $0.04 \mathrm{~mm}$ .

See Solution

Problem 76

Graph the functions: $y = 3|x-3|$ and $y = 2|x+1|-1$ . Explain how the equations affect the graph's shape.

See Solution

Problem 77

Find the domain and range of $f(x)=|3+3x|$ as intervals using parentheses and brackets.

See Solution

Problem 78

Express the interval $[-17,17]$ as an absolute value inequality for variable $x$ .

See Solution

Problem 79

Find the set $S=\{x:|x^{2}-6|>7\}$ as a union of intervals.

See Solution

Problem 80

Find the function with an axis of symmetry at $x = -3$ : $f(x)=|x-3|$ , $f(x)=|x|+3$ , $f(x)=|x+3|$ , $f(x)=|x|-3$ .

See Solution

Problem 81

Find the solution set for the equation: $-3|1-x|-2=-14$ . Options: $\{-5,3\}$ , $\{-3,5\}$ , $\{3,-5\}$ , $\{5,3\}$ .

See Solution

Problem 82

Solve the equation $-5+\left|\frac{x}{6}\right|=-7$ . What is the solution set?

See Solution

Problem 83

Solve the inequality $|2x-5|-3<-7$ and identify the solution set: $-5<x<-1$ , $x<-5$ or $x>-1$ , $\varnothing$ , or $R$ .

See Solution

Problem 84

Find the inequality that represents the range of $f(x)=|x-5|+3$ . Options: $y \geq-5$ , $y \geq-3$ , $y \geq 3$ , $y \geq 5$ .

See Solution

Problem 85

Evaluate $\left|c^{2}+b^{2}\right|$ for $a=5$ , $b=-3$ , and $c=-2$ .

See Solution

Problem 86

Solve the inequality $-3|x+2|<-9$ .

See Solution

Problem 87

Solve the equation: $|0.04 x-1|=6.04$

See Solution

Problem 88

Solve the inequality $|x-1400| \leq 100$ .

See Solution

Problem 89

Solve the inequality and express the solution set in interval notation: $|2x + 1| + 3 > 8$ .

See Solution

Problem 90

Find the absolute value of -11. What is $|-11|$ ?

See Solution

Problem 91

Use the Law of Syllogism to create a new conditional statement from these true statements: If $x<-2$ , then $|x|>2$ ; If $x>2$ , then $|x|>2$ .

See Solution

Problem 92

Find the function $g(x)$ that represents a horizontal shrink of $f(x)=|2x|+4$ by a factor of $\frac{1}{2}$ .

See Solution

Problem 93

Find $x$ where $f(x) = 3$ .

See Solution

Problem 94

Find $x$ such that $f(x) = -3$ for the function $f(x) = |x|$ .

See Solution

Problem 95

Calculate $f(-9)$ for the function $f(x)=|x|-6$ .

See Solution

Problem 96

Calculate $-f(x)$ for the function $f(x)=|x|-3$ .

See Solution

Problem 97

If Ann's house is at 0, and Beth is 4 blocks away, what are the possible locations for Carol's house, given she is 2 blocks from Beth?

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Problem 98

Define the function $g(x)$ based on the graph of $f(x)=|x|$ shifted left 1 unit and down 9 units.

See Solution

Problem 99

Write the equation for a function like $f(x)=|x|$ , shifted left 1 and down 9.
$g(x)=$

See Solution

Problem 100

Solve the inequality $4|t+3| \geq 8$ .

See Solution

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Absolute Value

Problem 1

Problem 2

Намери xxx от уравнението ∣32−24∣−x=∣513−556∣\left|3^{2}-2^{4}\right|-x=\left|5 \frac{1}{3}-5 \frac{5}{6}\right|∣∣​32−24∣∣​−x=∣∣​531​−565​∣∣​.

Problem 3

If ∣x−3∣>5|x-3|>5∣x−3∣>5, which inequalities are true? a) −2<x<8-2<x<8−2<x<8 b) −8<x<2-8<x<2−8<x<2 c) x<−8∪x>2x<-8 \cup x>2x<−8∪x>2 d) x<−2∪x>8x<-2 \cup x>8x<−2∪x>8 e) x<−8∪x>−2x<-8 \cup x>-2x<−8∪x>−2

Problem 4

Graph g(x)=∣x−2∣g(x)=|x-2|g(x)=∣x−2∣ and compare it to f(x)=∣x∣f(x)=|x|f(x)=∣x∣. Describe the domain and range. Select the correct translation and range.

Problem 5

Graph g(x)=−14∣x∣g(x)=-\frac{1}{4}|x|g(x)=−41​∣x∣. Compare to f(x)=∣x∣f(x)=|x|f(x)=∣x∣ and describe domain and range. Choose the correct option.

Problem 6

Describe the transformations from f(x)=∣x∣f(x)=|x|f(x)=∣x∣ to g(x)=2∣x+1∣−2g(x)=2|x+1|-2g(x)=2∣x+1∣−2 and graph g(x)g(x)g(x). Choose the correct transformation option.

Problem 7

Identify the transformations from f(x)=∣x∣f(x)=|x|f(x)=∣x∣ to g(x)=−∣x+2∣+3g(x)=-|x+2|+3g(x)=−∣x+2∣+3 and choose the correct description.

Problem 8

Jonael dropped a sandbag from a balloon 250 meters above a target. The bag is 75 meters below the balloon. Find 2 expressions for the distance to the target. Choose 2 answers: A ∣−250+75∣|-250+75|∣−250+75∣ B ∣−75+250∣|-75+250|∣−75+250∣ C ∣250+75∣|250+75|∣250+75∣

Problem 9

Find xxx such that 18−x−2x=x+2\sqrt{18-x}-\sqrt{2x}=\sqrt{x+2}18−x​−2x​=x+2​ and ∣x+1x−4∣<3\left|\frac{x+1}{x-4}\right|<3∣∣​x−4x+1​∣∣​<3.

Problem 10

Is the statement true or false: 19.7<∣19.7∣19.7 < |19.7|19.7<∣19.7∣? Answer: True O False

Problem 11

Find the number of solutions for the equation ∣x∣=75|x|=75∣x∣=75. Options: No Solution, One Solution, Two Solutions.

Problem 12

Solve the equation ∣x∣=−16|x| = -16∣x∣=−16. What is the solution set?

Problem 13

Find the range of the function f(x)=∣x∣−3f(x)=|x|-3f(x)=∣x∣−3. Options include f(x)≥−3f(x) \geq -3f(x)≥−3, f(x)<−3f(x) < -3f(x)<−3, f(x)≤−3f(x) \leq -3f(x)≤−3, f(x)>−3f(x) > -3f(x)>−3.

Problem 14

Solve the inequality ∣x−3∣≤5|x-3| \leq 5∣x−3∣≤5.

Problem 15

Determine the domain, range, intervals of increase/decrease, x-intercepts, and y-intercept for f(x)=2∣x+3∣−6f(x)=2|x+3|-6f(x)=2∣x+3∣−6.

Problem 16

Identify the absolute value parent function from the options: A. f(x)=∣2x∣f(x)=|2 x|f(x)=∣2x∣, B. f(x)=∣x∣f(x)=|x|f(x)=∣x∣, C. f(x)=∣x∣−2f(x)=|x|-2f(x)=∣x∣−2, D. f(x)=∣x∣+1f(x)=|x|+1f(x)=∣x∣+1.

Problem 17

Find the domain and range of the absolute value function: A. y<0y<0y<0, B. all reals, y≥0y \geq 0y≥0, C. y≥0y \geq 0y≥0, D. all reals, y>0y>0y>0.

Problem 18

Identify the equation that represents an absolute value function from these options: f(x)=−9f(x)=-9f(x)=−9, f(x)=13xf(x)=\frac{1}{3 x}f(x)=3x1​, f(x)=x−3x2f(x)=x-3 x^{2}f(x)=x−3x2, f(x)=−14∣x+4∣−3f(x)=\frac{-1}{4}|x+4|-3f(x)=4−1​∣x+4∣−3.

Problem 19

Analyze the function f(x)=∣x−3∣−1f(x)=|x-3|-1f(x)=∣x−3∣−1: find domain, range, intercepts, increasing/decreasing intervals, and end behavior.

Problem 20

Solve the equation −7∣3−6x∣−4=−67-7|3-6 x|-4=-67−7∣3−6x∣−4=−67.

Problem 21

Solve the equation ∣−9+2p∣4=2\frac{|-9+2 p|}{4}=24∣−9+2p∣​=2.

Problem 22

Solve for xxx in the equation 9+∣7+5x∣=619 + |7 + 5x| = 619+∣7+5x∣=61.

Problem 23

Solve the equation 1−8∣−5x+9∣=91 - 8|-5x + 9| = 91−8∣−5x+9∣=9.

Problem 24

Solve the equation −8∣−5x+9∣=9-8|-5 x+9|=9−8∣−5x+9∣=9.

Problem 25

Evaluate −4∣5+m∣-4|5+m|−4∣5+m∣ for m=−3m=-3m=−3. What is the result?

Problem 26

Identify the parent function and transformations for: y=2∣x+4∣+4y=2|x+4|+4y=2∣x+4∣+4.

Problem 27

Graph f(x)=∣x+2∣x+2f(x)=\frac{|x+2|}{x+2}f(x)=x+2∣x+2∣​ for the range [−4,4][-4,4][−4,4].

Problem 28

Solve for nnn in the equation 3∣2−5n∣=03|2-5n|=03∣2−5n∣=0.

Problem 29

Define the absolute value function f(x)=∣4x+7∣f(x)=|4x+7|f(x)=∣4x+7∣ as a piecewise function.

Problem 30

Solve the equation ∣5x+5∣−5=−10 \frac{|5 x+5|}{-5}=-10 −5∣5x+5∣​=−10.

Problem 31

Solve the equation: ∣x+13∣−2=−20\frac{|x+13|}{-2}=-20−2∣x+13∣​=−20.

Problem 32

Solve for xxx: −∣2x+2∣5=−10\frac{-|2 x+2|}{5}=-105−∣2x+2∣​=−10

Problem 33

Daniel spends around \$30 on gas at \$2.50 per gallon. Write an inequality to find the range of gallons he can buy.

Problem 34

Solve the equation ∣5y−4∣=7|5 y-4|=7∣5y−4∣=7.

Problem 35

Simplify the expression 15−z∣15−z∣\frac{15-z}{|15-z|}∣15−z∣15−z​ for the case when z<15z<15z<15.

Problem 36

Solve 10∣7x+7∣+10≥8010|7 x+7|+10 \geq 8010∣7x+7∣+10≥80 for xxx.

Problem 37

Find f(6+h)f(6+h)f(6+h) for f(x)=∣x−6∣x−6f(x)=\frac{|x-6|}{x-6}f(x)=x−6∣x−6∣​ when h<0h<0h<0.

Problem 38

Solve the inequality ∣9n+2∣+9≥47|9 n + 2| + 9 \geq 47∣9n+2∣+9≥47.

Problem 39

Find the min and max lengths for nails allowed to vary by 132\frac{1}{32}321​ inch from 1 inch. Is a 1.05 inch nail acceptable?

Problem 40

Evaluate ∣6x+4y∣|6x + 4y|∣6x+4y∣ for x=4x = 4x=4 and y=−1y = -1y=−1.

Намери $x$ от уравнението $\left|3^{2}-2^{4}\right|-x=\left|5 \frac{1}{3}-5 \frac{5}{6}\right|$ .

If $|x-3|>5$ , which inequalities are true? a) $-2<x<8$ b) $-8<x<2$ c) $x<-8 \cup x>2$ d) $x<-2 \cup x>8$ e) $x<-8 \cup x>-2$

Graph $g(x)=|x-2|$ and compare it to $f(x)=|x|$ . Describe the domain and range. Select the correct translation and range.

Graph $g(x)=-\frac{1}{4}|x|$ . Compare to $f(x)=|x|$ and describe domain and range. Choose the correct option.

Describe the transformations from $f(x)=|x|$ to $g(x)=2|x+1|-2$ and graph $g(x)$ . Choose the correct transformation option.

Identify the transformations from $f(x)=|x|$ to $g(x)=-|x+2|+3$ and choose the correct description.

Jonael dropped a sandbag from a balloon 250 meters above a target. The bag is 75 meters below the balloon. Find 2 expressions for the distance to the target. Choose 2 answers: A $|-250+75|$ B $|-75+250|$ C $|250+75|$

Find $x$ such that $\sqrt{18-x}-\sqrt{2x}=\sqrt{x+2}$ and $\left|\frac{x+1}{x-4}\right|<3$ .

Is the statement true or false: $19.7 < |19.7|$ ? Answer: True O False

Find the number of solutions for the equation $|x|=75$ . Options: No Solution, One Solution, Two Solutions.

Solve the equation $|x| = -16$ . What is the solution set?

Find the range of the function $f(x)=|x|-3$ . Options include $f(x) \geq -3$ , $f(x) < -3$ , $f(x) \leq -3$ , $f(x) > -3$ .

Solve the inequality $|x-3| \leq 5$ .

Determine the domain, range, intervals of increase/decrease, x-intercepts, and y-intercept for $f(x)=2|x+3|-6$ .

Identify the absolute value parent function from the options: A. $f(x)=|2 x|$ , B. $f(x)=|x|$ , C. $f(x)=|x|-2$ , D. $f(x)=|x|+1$ .

Find the domain and range of the absolute value function: A. $y<0$ , B. all reals, $y \geq 0$ , C. $y \geq 0$ , D. all reals, $y>0$ .

Identify the equation that represents an absolute value function from these options: $f(x)=-9$ , $f(x)=\frac{1}{3 x}$ , $f(x)=x-3 x^{2}$ , $f(x)=\frac{-1}{4}|x+4|-3$ .

Analyze the function $f(x)=|x-3|-1$ : find domain, range, intercepts, increasing/decreasing intervals, and end behavior.

Solve the equation $-7|3-6 x|-4=-67$ .

Solve the equation $\frac{|-9+2 p|}{4}=2$ .

Solve for $x$ in the equation $9 + |7 + 5x| = 61$ .

Solve the equation $1 - 8|-5x + 9| = 9$ .

Solve the equation $-8|-5 x+9|=9$ .

Evaluate $-4|5+m|$ for $m=-3$ . What is the result?

Identify the parent function and transformations for: $y=2|x+4|+4$ .

Graph $f(x)=\frac{|x+2|}{x+2}$ for the range $[-4,4]$ .

Solve for $n$ in the equation $3|2-5n|=0$ .

Define the absolute value function $f(x)=|4x+7|$ as a piecewise function.

Solve the equation $\frac{|5 x+5|}{-5}=-10$ .

Solve the equation: $\frac{|x+13|}{-2}=-20$ .

Solve for $x$ : $\frac{-|2 x+2|}{5}=-10$

Solve the equation $|5 y-4|=7$ .

Simplify the expression $\frac{15-z}{|15-z|}$ for the case when $z<15$ .

Solve $10|7 x+7|+10 \geq 80$ for $x$ .

Find $f(6+h)$ for $f(x)=\frac{|x-6|}{x-6}$ when $h<0$ .

Solve the inequality $|9 n + 2| + 9 \geq 47$ .

Find the min and max lengths for nails allowed to vary by $\frac{1}{32}$ inch from 1 inch. Is a 1.05 inch nail acceptable?

Evaluate $|6x + 4y|$ for $x = 4$ and $y = -1$ .

Solve the inequality: $10|7x + 7| + 10 \geq 80$ .

Evaluate $|f-71|$ for $f=-4$ .

Evaluate $32|r|-7$ for $r=-2$ .

Evaluate $q + 9|p|$ for $p=2$ and $q=-66$ .

Evaluate $m + 62|k|$ for $k = -1$ and $m = -59$ .

Evaluate $-4|w| + 630$ for $w = 83$ .

Solve the inequality $9|2 x-1|+4<49$ .

Find the graph of the inequality $|\frac{1}{2} x + 2| \geq 1$ .

Graph the inequality $\left|\frac{1}{2} x + 2\right| \geq 1$ .

Solve the equation $|3 x+5|=5 x+2$ . What are the possible values of $x$ ?

Solve: $8|3x-5|=56$ . Choose the correct solution set from: a. $\{-4\}$ b. $\left\{-4, \frac{2}{3}\right\}$ c. $\left\{-\frac{2}{3}, 4\right\}$ d. $\left\{4,-\frac{14}{3}\right\}$ .

Solve the inequality $|x-7|+12 \leq 25$ and select the correct solution set from the options given.

Solve the equation: $\left|\frac{5}{x-3}\right|=15$

Graph the piecewise function $p(x)$ defined as:
$p(x) = -2|x+6| + 7$ for $-8 \leq x < -3$ , $\frac{1}{3} x - 2$ for $-3 < x \leq 3$ , and $(x-5)^{2} - 5$ for $3 < x < 8$ .

Calculate $|2y-5|$ when $y = 5$ .

Solve for $z$ in the equation $7 - |3z + 10| = 0$ .

Calculate the expression $-|2(1.2)-4|$ .

Solve the equation $|x-3|=17$ .

Evaluate $3|x+4|+|3x|$ for $x = -4$ .

Solve the equation: $|x-3|=17$ .

Solve the equation $8|x-3|=88$ .

Solve the equation $|12+4 x|=16$ .

Solve the equation $|3 x-10|=17$ .

Graph the inequality $|4x + 2| < 10$ .

Solve $|5 x|=70$ . What are the possible values of $x$ ?

Find the vertex of the function $f(x)=|x-4|+3$ . What are the coordinates of the vertex?

Find the domain and range of the function $f(x)=|x-4|+3$ .

Find the function $g(x)$ that reflects $f(x)=|6x|-2$ in the $y$ -axis.

Solve the inequality $|x-1|-2x>1$ .

Find the value of $f(8)$ for the function $f(x)=|x-3|-5$ .

Solve for $x$ : $2|3 x-4|+15=43$

Graph the equation $y=-5|x|$ and describe its transformation from $f(x)=|x|$ . Choose the correct graph.

Graph the equation $y=-5|x|$ and describe the transformation from $f(x)=|x|$ . Choose the correct option.