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Pre-Algebra : Operations

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 #5 : Absolute Value

Evaluate:

$\left | -45 + \left (-83 \right ) \right | - 23$

Possible Answers:

105

None of the other responses is correct.

151

Correct answer:

105

Explanation:

$\left | -45 + \left (-83 \right ) \right | - 23$

$= \left | - \left (45+83 \right ) \right | - 23$

$= \left | - 128 \right | - 23$

= 128 - 23

= 105

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Example Question #4 : Absolute Value

Solve:

$4+\left | -8-5 \right |=$

Possible Answers:

Correct answer:

Explanation:

$4+\left | -8-5 \right |=4+\left | -13 \right |=4+13=17$

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Example Question #7 : Absolute Value

Evaluate for x = 9 :

$| \left | x - 18\right | - x|$

Possible Answers:

Correct answer:

Explanation:

Substitute 9 for and evaluate:

$| \left | x - 18\right | - x|$

$= | \left | 9 - 18\right | - 9|$

$= | \left | - \left (18- 9 \right ) \right | - 9|$

$= | \left | -9 \right | - 9|$

= | 9- 9|

= | 0 |

= 0

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Example Question #5 : Absolute Value

Evaluate for x = -6 :

| |20 + x | - 6 -x |

Possible Answers:

Correct answer:

Explanation:

Substitute for and evaluate:

| |20 + x | - 6 -x |

=| |20 + (-6) | - 6 -(-6) |

=| |20 -6 | - 6 -(-6) |

=|14- 6 -(-6) |

=|8 -(-6) |

=|8+6 |

=|14 |

= 14

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Example Question #9 : Absolute Value

Solve:

$\left | 3-8\right |=$

Possible Answers:

$\textup{No solution}$

Correct answer:

Explanation:

Explanation:

Step 1: Solve the problem

$\left | 3-8\right |=\left | -5\right |$

Step 2: Solve for the absolute value

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

Remember, absolute value refers to the total number of units, so it will always be positive. For instance, if I am $5 in debt, I have -$5, but the absolute value of my debt is $5, because that is the total number of dollars that I'm in debt.

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Example Question #5 : Absolute Value

Solve for .

$\left | x\right |=5$

Possible Answers:

$\pm5$

Correct answer:

$\pm5$

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two answers. x=5, x=-5

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Example Question #11 : Absolute Value

Solve for .

$\left | x+1\right |=3$

Possible Answers:

2, 3

-4, 2

Correct answer:

-4, 2

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two equations. -(x+1)=3, x+1=3

For the left equation, we can switch the minus sign to the other side to get x+1=-3 . When we subtract on both sides, we get x=-4 .

For the right equation, just subtract on both sides, we get x=2 .

x=2, x=-4

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Example Question #12 : Absolute Value

Solve for .

$\left | 4x\right |=12$

Possible Answers:

$\pm3$

Correct answer:

$\pm3$

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two equations. 4x=12, -(4x)=12

For the left equation, when we divide both sides by , x=3 .

For the right equation, we distribute the negative sign to get -4x=12 . When we divide both sides by , x=-3 .

x=3, x=-3

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Example Question #13 : Absolute Value

Solve for .

$\left | 2x\right |+5=9$

Possible Answers:

$\pm2$

-2, -4

Correct answer:

$\pm2$

Explanation:

When taking absolute values, we need to consider both positive and negative values. Let's first subtract on both sides. So, we have two equations. 2x=4, -(2x)=4

For the left equation, when we divide both sides by , x=2 .

For the right equation, we distribute the negative sign to get -2x=4 . When we divide both sides by , x=-2 .

x=2, x=-2

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Example Question #14 : Absolute Value

Solve for

$16+4x=4+2\left | x\right |$

Possible Answers:

2,6

-2, -6

Correct answer:

Explanation:

When taking absolute values, we need to consider both positive and negative values. So, we have two equations. 16+4x=4+2x, 16+4x=4-2x

For the left equation, we subtract on both sides and subtract on both sides. We now have 12=-2x . When we divide both sides by , x=-6 .

For the right equation, we subtract on both sides and subtract on both sides. We now have 12=-6x . When we divide both sides by , x=-2 .

Let's double check. When we plug in , both sides aren't equal.

$16+4(-6)=4+2\left | -6\right |$

16-24=4+12

$-8\neq16$

But if we plug in -2, we get both sides equal.

$16+4(-2)=4+2\left | -2\right |$

16-8=4+4

8=8

So is the only answer.

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Pre-Algebra : Operations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #5 : Absolute Value

Example Question #4 : Absolute Value

Example Question #7 : Absolute Value

Example Question #5 : Absolute Value

Example Question #9 : Absolute Value

Example Question #5 : Absolute Value

Example Question #11 : Absolute Value

Example Question #12 : Absolute Value

Example Question #13 : Absolute Value

Example Question #14 : Absolute Value

All Pre-Algebra Resources

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