Solving 2-Step Variable Equations

What??? Relax!! You’ve already learned 1-step! You’ll use what you already know to solve 2-step equations.

STEP 1 The first step – Simplify anything you may need to on each side of the equal sign. Look for things like the distributive property and like terms.

STEP 2 The second step – figure out the order that you would DO to solve if you knew the value of the variable.

STEP 3 The third step – is to UNDO those steps by working in reverse order using inverse operations! + - ÷ •

Whatever we do on one side, we have to do on the other. Let’s try a problem. Distributive? Like Terms? 8x + 5 = 61 So to UNDO: - 5 then… ÷ 8 - 5 - 5 We would first DO: · 8 then… + 5 so… = 56 8x Whatever we do on one side, we have to do on the other.

Now, Step 2. 8x = 56 Whatever we do on one side, we have to do on the other. This problem has multiplication, so we need to divide now. 8 8 x 7 =

Whatever we do on one side, we have to do on the other. Let’s try a problem. Distributive? Like Terms? -5x + 3 = 38 - 3 - 3 UNDO in reverse… - 3 ÷ (-5) DO originally… · (-5) + 3 = 35 -5x Whatever we do on one side, we have to do on the other.

Now, Step 2. -5x = 35 Whatever we do on one side, we have to do on the other. This problem has multiplication, so we need to divide now. -5 -5 x -7 =

Let’s try another problem. Distributive? Like Terms? + 9 + 9 DO originally… ÷ (-4) - 9 UNDO in Reverse… + 9 = 40 · (-4) Whatever we do on one side, we have to do on the other.

Now, Step 2.   This problem has division, so we need to multiply now. a = -160 Whatever we do on one side, we have to do on the other.

Let’s try another problem. Distributive? Like Terms?   DO originally… - 8 ÷ 3 UNDO in reverse… · 3 + 8   a - 8 = 12 Whatever we do on one side, we have to do on the other.

Now, Step 2. a - 8 = 12 + 8 + 8 a 20 = Whatever we do on one side, we have to do on the other.

Whatever we do on one side, we have to do on the other. Let’s try a problem. Distributive? Like Terms? -3x + 5x - 3 = 9 2x - 3 = 9 UNDO in reverse… + 3 ÷ 2 DO originally… · 2 - 3 + 3 + 3 2x = 12 Whatever we do on one side, we have to do on the other.

Now, Step 2. 2x = 12 2 2 x = 6 Whatever we do on one side, we have to do on the other.

Whatever we do on one side, we have to do on the other. Let’s try a problem. Distributive? Like Terms? 2(-3x – 14) = - 4 -6x - 28 = - 4 UNDO in reverse… + 28 ÷ (-6) DO originally… · (-6) - 28 + 28 + 28 -6x = 24 Whatever we do on one side, we have to do on the other.

Now, Step 2. -6x = 24 -6 -6 x = - 4 Whatever we do on one side, we have to do on the other.

Now you try some problems. Set up the DO/UNDO chart for each question. Solve and show all your work!   7f + 5 = 40        

Now you try some problems. Set up the DO/UNDO chart for each question. Solve and show all your work!   7f + 5 = 40 t=5 t = 186     y = -80 m = 100     x = -21 x = 3