Steps for Solving Equations with Variables on Both Sides

1. Distribute when necessary.

2. Combine like terms if possible.

3. Add or subtract to get the variables on one side of the equation. – move all variables to the left side of the equation until you get the hang of solving equations with variables on both sides.

4. Add or subtract to get the constants on one side of the equation.

– Move all constants to the right side of the equation.

5. Multiply or divide to solve for the variable.

Examples!!!!

Solve the equation. Check your answer.

1. 9x + 4 = 6x – 11 -6x -6x • Step 3 3x + 4 = -11 - 4 - 4 3x = -15 • Step 4 x = -5 • Step 5

Solve the equation. Check your answer.

2. 4b – 13 = 7b - 28 -7b -7b -3b – 13 = -28 + 13 +13 -3b = -15 b= 5 • Step 3 • Step 4 • Step 5

Solve the equation. Check your answer.

3. 7c – 4 = 9c - 11 -9c -9c -2c – 4 = -11 + 4 + 4 -2c = -7 c = 3.5

• Step 3 • Step 4 • Step 5

Solve the equation. Check your answer.

4. 3 – 4d = 6d - 17 - 6d -6d 3 – 10d = -17 - 3 - 3 -10d = -20 d = 2 • Step 3 • Step 4 • Step 5

Solve the equation. Check your answer.

5. 2(5 – 3s) = 2(8 + s) 10 – 6s = 16 + 2s - 2s 10 – 8s = 16 - 2s -10 -10 -8s = 6 s =  3 4 • Step 1 • Step 3 • Step 4 • Step 5

Solve the equation. Check your answer.

6. -5 (m + 1) = 22 + 4m -5m - 5 = 22 + 4m -4m -9m – 5 = 22 - 4m + 5 +5 -9m = 27 m = -3 • Step 1 • Step 3 • Step 4 • Step 5

Identity vs. No Solution

• When dealing with identity and no solution, all of your variables will cancel out. – When you solve the equation and come up with: • Some number = the same number : identity – Ex. 2 = 2 – identical – identity • A number = another number – Ex. 2 = 3 – not the same – no solution.

Identity vs. No Solution Solve until you have one number equal or not equal to another.

• 3 (a + 4) = 3a + 12 3a + 12 = 3a + 12 -3a -3a 12 = 12 – IDENTICAL!

IDENTITY!!!!!!!!

• 18r + 5 = 3 (5 + 6r) 18r + 5 = 15 + 18r -18r - 18r 5 = 15 – NEVER!!!

NO SOLUTION!!!!

More Practice!!!!

• Textbook – p. 99 # 28 - 33