1. 2
Understanding Variables and Solving Equations

2. R.1 Fractions
2.5 Solving Equations with Several Steps
Objectives
Solve equations using the addition and division properties of equality.
Solve equations using the distributive, addition, and division properties.

3. Solve equations using the addition and division properties of equality.

4. Solve equations using the addition and division properties of equality.
Example
Solve the equation 5m + 1 = 16. Check the solution.
Step 1
Add the same amount to both sides.

5. Solve equations using the addition and division properties of equality.
(continued)
Example
Step 2
Divide both sides by the coefficient.

6. (continued) Check the solution. Example
Solve equations using the addition and division properties of equality.
(continued) Check the solution.
Example
Step 3

7. Solve equations using the addition and division properties of equality.
Example
Solve the equation 2x – 2 = 5x – 11.
Add the same amount to both sides.
Add the same amount to both sides.
Divide both sides by –3.

8. Solve equations using the addition and division properties of equality.
Note
More than one sequence of steps will work. The basic approach is:
Simplify each side of the equation, if possible.
Get the variable term by itself on one side of the equal sign and a number by itself on the other side.
Divide both sides by the coefficient of the variable term.

9. Solve the equation –6 = 3(y – 2). Check the solution. Example
Solve equations using the distributive, addition, and division properties.
Solve the equation –6 = 3(y – 2). Check the solution.
Example
Use the distributive property to rewrite the equation.
Add the same amount to both sides.
Divide both sides by the coefficient.

10. Solve equations using the distributive, addition, and division properties.
(continued) Check the solution.
Example

11. Solve equations using the distributive, addition, and division properties.

12. Solve the equation 8 + 5(m +2) = 6 + 2m. Check the solution.
Solve equations using the distributive, addition, and division properties.
Solve the equation 8 + 5(m +2) = 6 + 2m. Check the solution.
Example
Step 1
Step 2

13. Solve equations using the distributive, addition, and division properties.
(continued)
Example
Step 3
Add 2m to both sides.
To get 3m by itself, add –18 to both sides.

14. Solve equations using the distributive, addition, and division properties.
(continued)
Example
Step 4
Divide both sides by 3, the coefficient of the variable term is 3m.
The solution is –4.

15. Solve equations using the distributive, addition, and division properties.
(continued)
Example
Step 5 Check