Multi-Step Equations Notes and Practice

Essential Question How do I solve an equation that has more than one variable term?

Multi-Step Equations Equations will not always be able to be solved in one or two steps. You will see many more complicated equations in higher math. 6 – x – 3 = 4(x – 2) + 4

Process Simplify both sides of the equation separately Add/subtract to get all variable terms to one side of the equation (stay fair and balanced!) Solve the remaining two-step equation

Example 2x – 5(x + 4) = -2 2x – 5x – 20 = -2 -3x – 20 = -2 +20 +20 -3x = 18 -3 -3 x = -6 Original problem Distribute -5 Combine like terms Add 20 to both sides Divide both sides by -3

Subtract 4 from both sides Divide both sides by 4 Example Original problem Add x to both sides Subtract 4 from both sides Divide both sides by 4 +x +x _ 4x + 4 = 14 -4 -4 _ 4x = 10 4 4 x = 5/2

Practice (Be sure to check your answer!) 1) 5y – 7 = 3y – 13 2) 4(w + 1) – 2 = 18 3) 7x + 3 – 12 = -x + 7 4) 3(x – 2) = 12 5) 2x + 4 + 3x = 20 + x + 8 6) 9p + 27 – 3p = 72 Compare with a partner!

What about that original problem? 6 – x – 3 = 4(x – 2) + 4 6 – x – 3 = 4x – 8 + 4 -x + 3 = 4x – 4 3 = 5x – 4 7 = 5x 7/5 = x x = 7 5

Essential Question How do I solve an equation that has more than one variable term?