Writing and Solving a Two-Step EquationEXAMPLE 2

The sum of 4 times a number plus –6 is 14. What is the number?

4 times a number and –6 is 14. Write a verbal model.

4 n + (–6) = 14 Translate.

4n – 6 = 14 Write equation.

4n – 6 + 6 = 14 + 6 Add 6 to each side.

4n = 20 Simplify.

4n4 = 20

4Divide each side by 4.

n = 5 Simplify.

ANSWER The number is 5.

Writing and Solving a Two-Step EquationEXAMPLE 3

You want to find how many pages you need to read per week in order to finish several books in six weeks. The books have a total of 1244 pages. You have already read 500 pages. How many pages do you have to read per week?

Reading

EXAMPLE 3

1244 = 6p + 500 Write an algebraic model.

1244 – 500 = 6p + 500 – 500 Subtract 500 from each side.

744 = 6p

SOLUTION

Let p be the number of pages to read per week.

Simplify.

Divide each side by 6744 = 6p6 6

124 = p Simplify.

ANSWER You have to read 124 pages per week.

Writing and Solving a Two-Step Equation

GUIDED PRACTICE for Examples 2 and 3

2. The difference of six times a number and 9 is -3.What is the number?

ANSWER The number is 1.

GUIDED PRACTICE

3. What If?

Suppose in Example 3 that you have read 714 pages and have five weeks left. How many pages do you have to read per week?

for Examples 2 and 3

ANSWER

You have to read 106 pages per week