1. Algebra 1 EOC Summer School Lesson 10: Solve Linear Equations and Inequalities

2. Introduction to Solving When solving equations, we are trying to find x. When solving inequalities, we are trying to find what values x can be (more than one answer).

3. Operations in Equations Before you can solve an equation you need to know what operations are active in each equation. Operations are: add, subtract, multiply, & divide Ex 1: 2x = 6 Ex 2: x – 3 = 9 Ex 3: 2x + 1 = 5 Read it out loud: 2 times x equals 6. multiply x minus 3 equals 9 subtract 2 times x plus 1 equals 5 multiply add

4. Inverse Operations To solve equations, we use inverse operations to “undo” the existing operations. Example: x + 12 = -6 x plus 12 equals -6 add To “undo” we will subtract 12 from each side. - 12 -12 x = -18 The equals sign divides the equation into two “sides.”

5. More than 1 operation at work Equations with more than 1 operation at work require more than 1 inverse operation to solve. Example: 3x – 1 = 14 3 times x minus 1 equals 14 Multiply To “undo” we will add 1 to each side and then divide by 3. + 1 3x = 15 subtract 3 x = 5

6. Substitute, then solve In the equation 2x – 3y = 13, find the value of x if y = 1. 2x – 3y = 13Substitute with parentheses 2x – 3(1) = 13Simplify 2x – 3 = 13Read and Solve + 3 2x = 16 2 x = 8

7. Solving Inequalities Single variable inequalities are solved the same way as equations BUT, there is 1 exception! If you multiply or divide the inequality by a negative value, you must flip the inequality over.

8. Example of Solving an Inequality 12  -2x + 4 12 is less than or equal to -2 times x plus 4 Multiply - 4 - 4 8  -2x add -2 -4  x Warning: Dividing by a Negative!