SOLVE THE ONE- OR TWO-STEP EQUATION THAT REMAINS, REMEMBERING THE T...

4. Solve the one- or two-step equation that remains, remembering the two previous properties.

Examples

Solve forxin each of the following equations:a. 3x– 5 = 10Add 5 to both sides of the equation: 3x– 5 + 5 = 10 + 5

3x

Divide both sides by 3:

3

¹⁵

3

x= 5b. 3 (x– 1) + x= 1Use distributive property to remove parentheses:3x– 3 + x= 1Combine like terms: 4x– 3 = 1Add 3 to both sides of the equation: 4x– 3 + 3 = 1 + 3

4x

Divide both sides by 4:

4

⁴

4

x= 1c. 8x– 2 = 8 + 3xSubtract 3xfrom both sides of the equation to move the variables to one side:8x– 3x– 2 = 8 + 3x– 3xAdd 2 to both sides of the equation: 5x– 2 + 2 = 8 + 2

5x

Divide both sides by 5:

5

¹⁰

5

x= 2

S o l v i n g L i t e r a l E q u a t i o n s

A literal equation is an equation that contains two or more variables. It may be in the form of a formula. Youmay be asked to solve a literal equation for one variable in terms of the other variables. Use the same stepsthat you used to solve linear equations.

3 4 2

Example

Solve for xin terms ofaand b: 2x+ b= aSubtract bfrom both sides of the equation: 2x+ b– b= a– b

2x

Divide both sides of the equation by 2:

2

^a

2

^b

x

^a

2

^b

S o l v i n g I n e q u a l i t i e s

Solving inequalities is very similar to solving equations. The four symbols used when solving inequalities areas follows:

■

is less than

■

is greater than

■

is less than or equal to

■

is greater than or equal toWhen solving inequalities, there is one catch: If you are multiplying or dividing each side by a negativenumber, you must reverse the direction of the inequality symbol. For example, solve the inequality–3x+ 6 18:–3x66186