Question

Solve. State the number of solutions.

a. 3/2x - 10 = 2

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

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

Answer 1

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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