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Pre-Algebra : Absolute Value

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #311 : Operations And Properties

Solve:

$\left | -6+4\right |\times7=$ $\displaystyle \left | -6+4\right |\times7=$

Possible Answers:

$\displaystyle 70$

$\displaystyle 14$

$\displaystyle -14$

$\displaystyle -70$

Correct answer:

$\displaystyle 14$

Explanation:

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Example Question #1 : Absolute Value

Solve:

$\left | 7-3\right |=$ $\displaystyle \left | 7-3\right |=$

Possible Answers:

$\displaystyle 10$

$\displaystyle 7$

$\displaystyle -4$

$\displaystyle 4$

$\displaystyle -10$

Correct answer:

$\displaystyle 4$

Explanation:

Step 1: solve the problem

Step 2: solve for absolute value

$\left | 4\right |=4$ $\displaystyle \left | 4\right |=4$

Remember, absolute value refers to the total number of units, so it will always be positive. For instance, if I am $4 in debt, I have -$4, but the absolute value of my debt is $4, because that is the total number of dollars that I'm in debt.

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Example Question #313 : Operations And Properties

Solve:

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

Possible Answers:

$\small -5$ $\displaystyle \small -5$

$\small 5$ $\displaystyle \small 5$

$\small -11$ $\displaystyle \small -11$

$\small 11$ $\displaystyle \small 11$

Correct answer:

$\small 5$ $\displaystyle \small 5$

Explanation:

First, solve the equation:

Next, account for the absolute value:

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

Therefore, the answer is $\small 5$ $\displaystyle \small 5$.

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Example Question #4 : Absolute Value

Solve the expression below:

$\small \small 19+\left |3*(-6) \right |$ $\displaystyle \small \small 19+\left |3*(-6) \right |$

Possible Answers:

$\small 72$ $\displaystyle \small 72$

$\small 36$ $\displaystyle \small 36$

$\small 37$ $\displaystyle \small 37$

$\small -1$ $\displaystyle \small -1$

$\small 1$ $\displaystyle \small 1$

Correct answer:

$\small 37$ $\displaystyle \small 37$

Explanation:

$\small \small \small 19+\left |3*(-6) \right |$ $\displaystyle \small \small \small 19+\left |3*(-6) \right |$ simplifies to $\small \small \small \small 19+\left |-18 \right |$ $\displaystyle \small \small \small \small 19+\left |-18 \right |$

For absolute value expressions, the value within the bars is treated as positive

So, the expression becomes $\small 19+18$ $\displaystyle \small 19+18$ which adds to $\small 37$ $\displaystyle \small 37$

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Example Question #5 : Absolute Value

Evaluate:

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

Possible Answers:

151 $\displaystyle 151$

$\displaystyle -61$

None of the other responses is correct.

$\displaystyle 15$

105 $\displaystyle 105$

Correct answer:

105 $\displaystyle 105$

Explanation:

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

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

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

$\displaystyle = 128 - 23$

= 105 $\displaystyle = 105$

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Example Question #2 : Absolute Value

Solve:

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

Possible Answers:

$\displaystyle 7$

$\displaystyle -9$

$\displaystyle 17$

$\displaystyle 1$

Correct answer:

$\displaystyle 17$

Explanation:

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Example Question #6 : Absolute Value

Evaluate for x = 9 $\displaystyle x = 9$:

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

Possible Answers:

$\displaystyle 18$

$\displaystyle -9$

$\displaystyle -18$

$\displaystyle 36$

$\displaystyle 0$

Correct answer:

$\displaystyle 0$

Explanation:

Substitute 9 for $\displaystyle x$ and evaluate:

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

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

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

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

$\displaystyle = | 9- 9|$

= | 0 | $\displaystyle = | 0 |$

= 0 $\displaystyle = 0$

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Example Question #3 : Absolute Value

Evaluate for x = -6 $\displaystyle x = -6$:

$\displaystyle | |20 + x | - 6 -x |$

Possible Answers:

$\displaystyle 26$

$\displaystyle -2$

$\displaystyle 38$

$\displaystyle 2$

$\displaystyle 14$

Correct answer:

$\displaystyle 14$

Explanation:

Substitute $\displaystyle -6$ for $\displaystyle x$ and evaluate:

$\displaystyle | |20 + x | - 6 -x |$

$\displaystyle =| |20 + (-6) | - 6 -(-6) |$

$\displaystyle =| |20 -6 | - 6 -(-6) |$

$\displaystyle =|14- 6 -(-6) |$

$\displaystyle =|8 -(-6) |$

=|8+6 | $\displaystyle =|8+6 |$

=|14 | $\displaystyle =|14 |$

= 14 $\displaystyle = 14$

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Example Question #8 : Absolute Value

Solve:

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

Possible Answers:

$\displaystyle 5$

$\displaystyle 11$

$\displaystyle -5$

$\textup{No solution}$ $\displaystyle \textup{No solution}$

$\displaystyle -11$

Correct answer:

$\displaystyle 5$

Explanation:

Explanation:

Step 1: Solve the problem

Step 2: Solve for the absolute value

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

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 #4 : Absolute Value

Solve for $\displaystyle x$.

$\left | x\right |=5$ $\displaystyle \left | x\right |=5$

Possible Answers:

$\displaystyle 5$

$\displaystyle 0$

$\pm5$ $\displaystyle \pm5$

$\displaystyle -5$

$\displaystyle 2$

Correct answer:

$\pm5$ $\displaystyle \pm5$

Explanation:

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

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Pre-Algebra : Absolute Value

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #311 : Operations And Properties

Example Question #1 : Absolute Value

Example Question #313 : Operations And Properties

Example Question #4 : Absolute Value

Example Question #5 : Absolute Value

Example Question #2 : Absolute Value

Example Question #6 : Absolute Value

Example Question #3 : Absolute Value

Example Question #8 : Absolute Value

Example Question #4 : Absolute Value

All Pre-Algebra Resources

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