Benchmark 8 Solving MultiStep Linear Equations 1 Solve

Benchmark #8 Solving Multi-Step Linear Equations

1) Solve. 8 y – 9 = -3 y + 2 You need to get the variables on one side of the equation. It ALWAYS try to move the SMALLER variable!

1. 2. 3. 4. 5. 6. 7. 1) Solve 8 y - 9 = -3 y + 2 + 3 y Draw “the river” 11 y – 9 = 2 Add 3 y to both sides Simplify +9 +9 Add 9 to both sides Simplify 11 y = 11 Divide both sides by 11 Simplify 11 11 y=1

1. 2) Solve 4 = 7 x - 3 x Draw “the river” 4 = 4 x – Notice the variables 4 4 are on the same side! Combine like terms 1=x Divide both sides by 4 2. 3. 4. Simplify

3) Solve -7(x - 3) + 3 = -7 1. 2. 3. 4. Draw “the river” Distribute Combine like terms Subtract 24 from both sides 5. Divide both sides by -7

What is the value of x if 3(x + 4) = 2(x - 1)? 1. 2. 3. 4. -14 -13 13 14 Answer Now

$4) Solve 1. 2. 3. 4. 5. Draw “the river” Clear the fraction –$

4) Solve 1. 2. 3. 4. 5. Draw “the river” Clear the fraction – multiply each term by the LCD Simplify Subtract 40 from both sides Divide by -8

5) Solve 1. 2. 3. 4. 5. 6. 7. 8. 9. Draw “the river” Clear the fraction – multiply each term by the LCD Simplify Add 2 x to both sides Simplify Add 6 to both sides Simplify Divide both sides by 6 Simplify 3 - 2 x = 4 x – 6 + 2 x +2 x 3 = 6 x – 6 +6 +6 9 = 6 x 6 6 or 1. 5 = x

Special Case #1 6) 2 x + 5 = 2 x - 3 1. Draw “the river” 2. Subtract 2 x from both sides 3. Simplify -2 x 5 = -3 This is never true! No solutions

Special Case #2 7) 3(x + 1) - 5 = 3 x - 2 1. 2. 3. 4. Draw “the river” Distribute Combine like terms Subtract 3 x from both sides 5. Simplify 3 x + 3 – 5 = 3 x - 2 = 3 x – 2 -3 x -2 = -2 This is always true! Infinite solutions or identity