Operations - Pre-Algebra

Step 1: solve the problem

Step 2: solve for absolute value

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.

First, solve the equation:

Next, account for the absolute value:

Therefore, the answer is .

Explanation:

Step 1: Solve the problem

Step 2: Solve for the absolute value

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.

simplifies to

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

So, the expression becomes which adds to

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.

Solve.

Substitute 9 for and evaluate:

Substitute for and evaluate:

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

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 .

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

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 .

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 , .

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 , .

When taking absolute values, we need to consider both positive and negative values. Let's multiply both sides 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 , .

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 , .

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.

But if we plug in we get both sides equal.

So is the only answer.

Let's isolate the variable by subtracting both sides by . We have:

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.