Algebra 1 EOC Summer School Lesson 10 Solve

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

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).

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 Read it out loud: 2 times x equals 6. • Ex 1: 2 x = 6 • Ex 2: x – 3 = 9 x minus 3 equals 9 multiply • Ex 3: 2 x + 1 = 5 subtract 2 times x plus 1 equals 5 multiply add

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

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

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

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. < >

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