Solve. State the number of solutions.

a. 3/2x - 10 = 2

b. 2 (2x-2) = 4x - 4

c. 3 (x+1) = 4x + 7 - x

a. x=8

b. Step 1: Simplify both sides of the equation.

2 (2x-2) = 4x-4

(2) (2x) + (2) (-2) = 4x+-4 (Distribute)

4x+-4=4x+-4

4x-4=4x-4

Step 2: Subtract 4x from both sides.

4x-4-4x=4x-4-4x

-4=-4

Step 3: Add 4 to both sides.

-4+4=-4+4

0=0

Answer:

All real numbers are solutions.

c. Step 1: Simplify both sides of the equation.

3 (x+1) = 4x+7-x

(3) (x) + (3) (1) = 4x+7+-x (Distribute)

3x+3=4x+7+-x

3x+3 = (4x+-x) + (7) (Combine Like Terms)

3x+3=3x+7

3x+3=3x+7

Step 2: Subtract 3x from both sides.

3x+3-3x=3x+7-3x

3=7

Step 3: Subtract 3 from both sides.

3-3=7-3

0=4

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