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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #15 : Absolute Value

Solve for

$3-\left | x\right |=5$

Possible Answers:

$\pm2$

No possible answer

Correct answer:

No possible answer

Explanation:

Let's isolate the variable by subtracting both sides by . We have:

$-\left | x\right |=2$ This will be a contradicting expression. Absolute values always generate positive values and since there's a negatie sign in front of it, it will never match a positive value. Therefore no possible answer exist.

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Example Question #16 : Absolute Value

Solve for .

$\left | x\right |-6=0$

Possible Answers:

$\pm6$

Correct answer:

$\pm6$

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two equations. -x-6=0, x-6=0

For the left side, we add to both sides and shift the negative sign to the other side to get x=-6 .

For the right side, we add to both sides and x=6 .

x=6, x=-6

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Example Question #17 : Absolute Value

Solve for .

$6+\left | x\right |=0$

Possible Answers:

$\pm6$

No possible answer

Correct answer:

No possible answer

Explanation:

Let's isolate the variable by subtracting both sides by . We have:

$\left | x\right |=-6$ This will be a contradicting expression. Absolute values always generate positive values. Therefore no possible answer exist.

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Example Question #18 : Absolute Value

Solve for .

$\frac{6}{\left | x\right |}=9$

Possible Answers:

$\frac{3}{2}$

$\pm \frac{3}{2}$

$\frac{2}{3}$

$\pm \frac{2}{3}$

Correct answer:

$\pm \frac{2}{3}$

Explanation:

When taking absolute values, we need to consider both positive and negative values. Let's multiply both sides by $\left | x\right |$ to get rid of the fraction. So, we have two equations. 9x=6, -(9x)=6

For the left equation, when we divide both sides by , $x=\frac{2}{3}$ .

For the right equation, we distribute the negative sign to get -9x=6 . When we divide both sides by , $x=-\frac{2}{3}$ .

$x=\frac{2}{3}, x=-\frac{2}{3}$

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Example Question #19 : Absolute Value

Solve for .

$\frac{\left | 4x\right |}{3}=8$

Possible Answers:

$\frac{1}{6}$

$\pm6$

$\pm \frac{1}{6}$

Correct answer:

$\pm6$

Explanation:

When taking absolute values, we need to consider both positive and negative values. Let's multiply each side by to get rid of the fraction. So, we have two equations. 4x=24, -(4x)=24

For the left equation, when we divide both sides by , x=6 .

For the right equation, we distribute the negative sign to get -4x=24 . When we divide both sides by , x=-6 .

x=6, x=-6

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Example Question #20 : Absolute Value

Solve for .

$\left | x\right |=17$

Possible Answers:

0, 17

$\pm17$

Correct answer:

$\pm17$

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two answers. x=17, x=-17

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Example Question #21 : Absolute Value

Solve for .

$\left | x+4\right |=6$

Possible Answers:

2, -10

2, 6

Correct answer:

2, -10

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two equations. x+4=6 and x+4=-6

For the left equation, we can subtract on both sides to get x=2 .

For the right equation, we can subtract on both sides to get x=-10 .

x=2, x=-10

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Example Question #21 : Absolute Value

Evaluate: $\left | 3-5 \right |$

Possible Answers:

Correct answer:

Explanation:

First, do 3-5 . This gives us . The absolute value function takes that negative and gives us back a positive .

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Example Question #23 : Absolute Value

Evaluate the following expression:

$\left |-3-5 \right |$

Possible Answers:

$-\left | 2\right |$

Correct answer:

Explanation:

The absolute value is the expression's distance from 0. The absolute value will give a positive number since distance cannot be a negative number.

$\left |-3-5 \right |$

$=\left |-8\right |$

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Example Question #24 : Absolute Value

Which of the following answers contain a number or numbers with an absolute value of fifteen?

Possible Answers:

and

150 and

Correct answer:

and

Explanation:

We can think of the absolute value of a number as describing the distance of that number from zero on the number line. Both and are numbers away from zero, but in opposite directions. Therefore, this is the correct answer.

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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #15 : Absolute Value

Example Question #16 : Absolute Value

Example Question #17 : Absolute Value

Example Question #18 : Absolute Value

Example Question #19 : Absolute Value

Example Question #20 : Absolute Value

Example Question #21 : Absolute Value

Example Question #21 : Absolute Value

Example Question #23 : Absolute Value

Example Question #24 : Absolute Value

All Pre-Algebra Resources

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