Solving MultiStep Equations Intro to Algebra Important In

Solving Multi-Step Equations Intro to Algebra

Important In order to solve multi-step equations we must remember how to: 1. Distribute 2. Combine Like Terms

Remember this… -3(x + 4) = -3(x) + (-3)(4) = -3 x + (-12) -2 a – 3 + 4 a + 8 -2 a + 4 a + (-3) + 8 = 2 a + 5

Remember this… -4 a – 3(a + 8) -4 a +(-3)(a + 8) -4 a + (-3 a) + (-24) -7 a + (-24)

Rules for Solving Multi-Step Equations

How can you get the “unknown” by itself? 8 x - 3 x - 10 = 20

Solving Multi-Step Equations… Isolate the variable! Get ‘x’ by itself. 8 x – 3 x – 10 = 20 5 x – 10 = 20 Combine like terms. 5 x – 10 + 10 = 20 + 10 Add 10 to each side. 5 x = 30 Simplify. 5 x = 30 5 5 Divide each side by 5. x=6 Simplify.

Check Your Work! 8 x – 3 x – 10 = 20 x =6 8(6) – 3(6) – 10 = 20 Are both sides equal?

Solve by Combining Like Terms 1. 9 – y + 6 y = -6 2. g + 8 g – 5 = -1 3. x + 2 x + 3 x – 7 = -25

Guided Practice • 1) 6 x – 2 x + 11 = -5 4 x = -16 x = -4 n 2) p – 17 p – 6 = -38 -16 p = -32 p=2

Solve Using Distribution 1. 2(x – 3) = 10 2. 2(a + 3) = -12 3. -3(p + 2) = 18

Solving Multi-Step Equations Using the Distributive Property… 6 x – 2(x – 5) = 46 Distributive property. 6 x – 2 x + 10 = 46 Combine like terms. 4 x + 10 = 46 4 x + 10 – 10 = 46 – 10 4 x = 36 4 x 36 = 4 4 x= 9 Subtract 10 from each side. Simplify. Divide each side by 4. Simplify.

Check Your Work! 6 x – 2(x – 5) = 46 x =9 6(9) – 2(9 – 5) = 46 Are both sides equal?

Guided Practice 6 x – 2(x + 11) = -6 6 x + (-2 x) + (-22) = -6 4 x = 16 x=4

Guided Practice 27 = 3 c – 3(6 – 2 c) 27 = 3 c + (-18) + 6 c 27 = 9 c + (-18) 45 = 9 c 5=c

Solving More Complicated Equations 1. 2(c – 3) – c = 9 2. 2(d + 3) + d = 12 3. 23 = 11 – (6 + k) – 2 k