Math - How to do absolute value in pre-algebra

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

Explanation

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

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

Explanation

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

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

$\frac{3}{4}$

Explanation

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, $\left | 3^2-12\right |=\left |-3 \right |=3.$

Solve the expression below.

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

Explanation

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

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

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

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

$2\tfrac{1}{2}$

Explanation

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 $\left | -5+3\right |=\left | -2\right |=2.$

Solve the absolute value expression.

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

Explanation

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

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.

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

$\small 30+14=44$

Is the inequality below true or false?

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

True

False; the sign should be changed to "less than"

The answer cannot be determined

False; the two terms are equal

Explanation

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.

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

$\frac{1}{2}$

Explanation

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 $\left | 12+24\right |=\left | 36\right |=36.$

What is the absolute value of ?

Explanation

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 .

Evaluate the expression.

$\left | 3-5\right |$

Explanation

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.

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

How to do absolute value in pre-algebra

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