Brandon and Felicia sold rolls of wrapping paper for a school fundraiser. Brandon sold 3 less than half the number of rolls that Felicia sold. Brandon sold a total of 9 rolls of wrapping paper.

Write an algebraic equation to represent , Remember that \begin{align*}w\end{align*}

In this concept, you will solve equations involving inverse properties of subtraction and division.

### Inverse Properties of Subtracting and Dividing

To solve a two-step equation, you will need to use more than one inverse operation. You begin solving two-step equations by isolating the variable.

For example, solve for

.

Your first step should be to use inverse operations to get the term that includes a variable, equation, 7 is subtracted from . So, you can use the inverse of subtraction—addition. Therefore, add 7 to both sides of the equation.

, by itself on one side of the equal sign. In the

Next, you can use inverse operations to isolate

. Since is divided by 6, you can use the inverse of division – multiplication.

The answer is 60.

Let’s review your steps to solving this two-step equation.

### Examples

#### Example 1

Earlier, you were given a problem about Brandon and Felicia’s fundraising.

Brandon sold 3 less than half of Felicia’s total, which was 9 rolls of wrap.

First, use the key words from the question to help you translate the problem into an equation. Remember that \begin{align*}w\end{align*} is the number of rolls of wrap.

So the equation is

.Next, use the inverse of subtraction—addition to isolate the variable.

Then, you can use inverse operations to isolate

. Since is divided by 2, you can use the inverse of division – multiplication.

The answer is 24.

Felicia sold 24 rolls of wrapping paper.

#### Example 2

First, use the inverse of subtraction—addition to isolate the variable.

Next, you can use inverse operations to isolate

. Since is divided by 6, you can use the inverse of division – multiplication.

The answer is 102.

#### Example 3

First, use the inverse of subtraction—addition to isolate the variable.

Next, you can use inverse operations to isolate

. Since is divided by 3, you can use the inverse of division – multiplication.

The answer is 51.

#### Example 4

First, use the inverse of subtraction—addition to isolate the variable.

Next, you can use inverse operations to isolate

. Since is divided by 73, you can use the inverse of division – multiplication.

The answer is 105.

#### Example 5

First, use the inverse of subtraction—addition to isolate the variable.

Next, you can use inverse operations to isolate

. Since is divided by 7, you can use the inverse of division – multiplication.

The answer is 98.

### Review

Solve each two-step equation that has division and subtraction in it.