How to do absolute value in pre-algebra - High School Math

Card 0 of 13

Question

Evaluate $\left | -6+5-2 \right |$

Answer

To solve problems with absolute value, first solve inside the absolute value signs. .

The absolute value of is because the negative sign is inside the absolute value signs. Remember the absolute value is the distance from that number to zero on the number line. Therefore, the absolute value is always positive.

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Question

Solve the expression below.

$7+\left | 5-9 \right |$

Answer

$7+\left | 5-9 \right |=7+\left | {-4} |$

For an absolute value, the term inside the bars will always become positive.

$7+\left | -4 \right |=7+4=11$

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Question

Solve the expression below.

$6-3\left | 4- 6 \right |_.$

Answer

$6-3\left | 4-6 \right |=6-3\left | -2 \right |$

For an absolute value, the term inside the bars will always become positive.

$6-3\left | -2 \right |=6-3(2)=6-6=0$

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Question

Solve the absolute value expression.

$\small \small 6\left | 3-8 \right |+14$

Answer

$\small \small 6\left | 3-8 \right |+14$

Simplify the absolute value, as if it were a parenthesis.

$\small \small 6\left | -5 \right |+14$

The absolute value of is . Remember that absolute values are always positive.

$\small (6)(5)+14$

$\small 30+14=44$

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Question

Is the inequality below true or false?

$\small \small \left | -7 \right |>12-6$

Answer

An absolute value is always the positive solution.

$\small \left | -7 \right |=7$

We can compare the terms by substituting the positive value of , and solving the right side of the inequality.

$\small \small \small \left | -7 \right |>12-6$

$\small \left | -7 \right |>6$

$\small 7>6$

The inequality is a true expression.

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Question

Evaluate the expression.

$\left | 3-5\right |$

Answer

First, treat the absolute value as a parenthesis, and evaluate the term inside.

$\left | 3-5\right |$

$\left | -2\right |$

The absolute value of any term is its distance from zero. A distance cannot be negative, thus, any negative term in an absolute value will be converted to a positive term.

$\left | -2\right |=2$

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Question

$14-\left | -3\right |*2$

Answer

The absolute value signs around negative 3 make it positive 3. Then following the order of operations:

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Question

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

Answer

The absolute value of a number can be thought of as its distance from zero. is three units away from zero. Therefore, $\left |-3 \right |=3$ .

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Question

$\left | 3^2-12\right |=?$

Answer

The absolute value of a number can be thought of as its distance from zero.

We start by solving the expression inside the absolute value signs and then measure how far that is from zero.

$\left | 3^2-12\right |$

$=\left | 9-12\right |$

$=\left | -3\right |$

is three units away from zero. Therefore, $\left | 3^2-12\right |=\left |-3 \right |=3.$

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Question

$\left | -5+3\right |=?$

Answer

The absolute value of a number can be thought of as its distance from zero.

We start by solving the expression inside the absolute value signs and then measure how far that is from zero.

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

$=\left | -2\right |$

is two units away from zero. Therefore $\left | -5+3\right |=\left | -2\right |=2.$

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Question

$\left | 12+24\right |=?$

Answer

The absolute value of a number can be thought of as its distance from zero.

We start by solving the expression inside the absolute value signs and then measure how far that is from zero.

$\left | 12+24\right |$

$=\left | 36\right |$

is units away from zero. That means that $\left | 12+24\right |=\left | 36\right |=36.$

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Question

What is ?

Answer

The absolute value of or, mathematically, , measures the distance between the number and zero. Since is three units away from zero, the absolute value will be .

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Question

What is the absolute value of ?

Answer

Recall that absolute value describes the distance a number is from . As a result of this, absolute value is always positive. Then, we have that the absolute value of must be .

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