Lesson 3-2

Solving Equations by Using Addition and Subtraction

Objectives

• Solve equations by using addition

• Solve equations by using subtraction

Vocabulary

• Equivalent equation – equations that have the same solution

• Solve an equation – find all values of the variable that make the equation a true statement

Addition and Subtraction PoE

Properties of Equality (PoE) are based on the concept that as long as you do the same thing to both sides of an equation, then you have not changed anything.

• Addition PoE

– For any numbers a, b, and c, if a = b, then a + c = b + c– You can add the same thing to both sides of an equation

without changing it.

• Subtraction PoE

– For any numbers a, b, and c, if a = b, then a - c = b - c– You can subtract the same thing from both sides of an

equation without changing it.

Example 1

Solve h – 12 = -27. Then check your solution.

Original equation

Answer: and

To check that –15 is the solution, substitute –15 for h in the original equation.

Add 12 to each side.

Example 2

Solve k + 63 = 92. Then check your solution.

To check that 29 is the solution, substitute 29 for k in the original equation.

Original equation

Answer: and

Add –63 to each side.

Example 3

Solve c + 102 = 36. Then check your solution.

To check that –66 is the solution, substitute –66 for c in the original equation.

Original equation

Answer: and

Subtract 102 from each side.

Example 4Write an equation for the problem. Then solve the equation and check your solution.

Fourteen more than a number is equal to twenty-seven. Find this number.

Fourteen more than a number is equal to twenty-seven.

Original equation

14 n 27

Subtract 14 from each side.

To check that 13 is the solution, substitute 13 for n in the original equation.

The solution is 13.

andAnswer:

Example 5

History The Washington Monument in Washington, D.C., was built in two phases. From 1848–1854, the monument was built to a height of 152 feet. From 1854 until 1878, no work was done. Then from 1878 to 1888, the additional construction resulted in its final height of 555 feet. How much of the monument was added during the second construction phase?

Example 5 cont

Answer: There were 403 feet added to the Washington Monument from 1878 to 1888.

Words The first height plus the additional height equals 555 feet.

Variables Let a = the additional height.

The first height plus the additional height equals 555.

Original equation

and

152 a 555

Subtract 152 from each side.

Summary & Homework

• Summary:– You can add the same thing to both sides of an

equation without changing it– You can subtract the same thing from both sides

of an equation without changing it– We can solve equations using these properties

• Homework: – page 132; 16-64 even