Absolute Value

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Pre-Algebra › Absolute Value

Questions 1 - 10

Solve the expression: $-\left | 3\cdot2\right |-3\left | -2\right |$

Explanation

To solve this, first evaluate the terms inside the absolute values.

Recall that any value inside an absolute value sign will become positive and the absolute value bars will go away.

$-\left | 3\cdot2\right |-3\left | -2\right | = -(6)-3(2)$

Simplify.

Solve for

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

No possible answer

$\pm2$

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.

Fill in the blank using $<, >, \leq, \geq, \text{or} =$ .

$\left | -9 \right | \square \ 4$

$\geq$

$\leq$

Explanation

The term $\left | -9\right |$ displays an absolute value. Absolute value is defined as the distance of a number in relation to zero on a number line. Since it is a distance, an absolute value cannot be negative. So,

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

So, we can rewrite the orignal problem as

$9\ \square \ 4$

and we can easily see that

Solve:

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

Explanation

Solve by evaluating the quantity inside the absolute value.

Remember that the absolute value bars will turn any value inside of them to a positive value.

Now simplify the absolute value, and apply order of operations.

$\ -\left | -3^2\right |^3 = -\left | -9 |^3 \ = -(9)^3 = -(9\times 9\times 9) \= -729$

Simplify the following:

$\left | -4\right |+4-\left | 2\right |+12$

None of the above

Explanation

It is important to be careful of where the negative sign is when simplifying.

When simplifying you should end up with:

which equals

Solve: $\left | -9(-9)\right |-\left | -18\right |$

Explanation

Simplify the terms inside the absolute value.

Negative and positive values inside the absolute value will become positive.

$\left | 81\right |-\left | 18\right | = 81-18 = 63$

Solve for .

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

$\pm6$

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

$\frac{1}{6}$

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.

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

For the right equation, we distribute the negative sign to get . When we divide both sides by , .

Solve: $-3\left | -1\right |-2\left | 1-2\right |$

Explanation

Evalute the absolute values first. Any negative or positive value inside a absolute value will be converted to a positive number.

$-3\left | -1\right |-2\left | 1-2\right | = -3(1)-2(1) = -3-2 = -5$

Solve:

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

Explanation

Step 1: solve the problem

$\left | 7-3\right |=\left | 4\right |$

Step 2: solve for absolute value

$\left | 4\right |=4$

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.

Solve:

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

$\textup{No solution}$

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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