Absolute Value - Pre-Algebra

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Question

Solve:

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

Answer

$\left | -6+4\right |\times7=\left | -2\right |\times7=2\times7=14$

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Question

Simplify the following:

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

Answer

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

When simplifying you should end up with:

which equals

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Question

Solve:

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

Answer

First, solve the equation:

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

Next, account for the absolute value:

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

Therefore, the answer is $\small 5$ .

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Question

Solve:

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

Answer

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.

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Question

Solve:

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

Answer

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

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Question

Solve:

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

Answer

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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Question

Solve the expression below:

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

Answer

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

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

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

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Question

Evaluate:

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

Answer

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

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

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

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Question

If , what is the value of ?

Answer

Substitute 5 for in the given equation and evaluate.

Remember that the absolute value of a number is its distance from zero on a number line. Distance is always positive; therefore, you can rewrite the expression.

Subtracting a positive number from a negative number is the same as adding a negative number.

$|-18 - 23|= |-18 +\left ( - 23 \right )|$

$|-18 +\left ( - 23 \right )|= |-\left (18 + 23 \right )|$

$|-\left (18 + 23 \right )|= |- 41|$

Solve.

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Question

Evaluate for :

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

Answer

Substitute 9 for and evaluate:

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

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

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

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

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Question

Evaluate for :

Answer

Substitute for and evaluate:

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Question

Solve for .

$\left | x\right |=5$

Answer

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

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Question

Solve for .

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

Answer

When taking absolute values, we need to consider both positive and negative values. So, we have two equations.

For the left equation, we can switch the minus sign to the other side to get . When we subtract on both sides, we get .

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

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Question

Solve for .

$\left | x\right |=17$

Answer

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

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Question

Solve for .

$\left | x+4\right |=6$

Answer

When taking absolute values, we need to consider both positive and negative values. So, we have two equations. and

For the left equation, we can subtract on both sides to get .

For the right equation, we can subtract on both sides to get .

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Question

Solve for .

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

Answer

When taking absolute values, we need to consider both positive and negative values. 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 , .

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Question

Solve for .

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

Answer

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.

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 , .

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Question

Solve for .

$\frac{6}{\left | x\right |}=9$

Answer

When taking absolute values, we need to consider both positive and negative values. Let's multiply both sides by $\left | x\right |$ to get rid of the fraction. So, we have two equations.

For the left equation, when we divide both sides by , $x=\frac{2}{3}$ .

For the right equation, we distribute the negative sign to get . When we divide both sides by , $x=-\frac{2}{3}$ .

$x=\frac{2}{3}, x=-\frac{2}{3}$

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Question

Solve for .

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

Answer

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 , .

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Question

Solve for

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

Answer

When taking absolute values, we need to consider both positive and negative values. So, we have two equations.

For the left equation, we subtract on both sides and subtract on both sides. We now have . When we divide both sides by , .

For the right equation, we subtract on both sides and subtract on both sides. We now have . When we divide both sides by , .

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

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

$-8\neq16$

But if we plug in we get both sides equal.

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

So is the only answer.

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