Question

An equation is shown below:

5(2x – 3) = 5

Part A: How many solutions does this equation have? (4 points)

Part B: What are the solutions to this equation? Show your work. (6 points)

Answer 1

Part A:

It has One Solution

Part B:

Step 1: 5(2x - 3) = 5

Step 2: (5 x 2x) - (5 x 3) = 5

Step 3: 10x - 15 = 5

Step 4: 10x - (15 + 15) = 5 + 15

Step 5: 10x - 0 = 20

Step 6: 10x = 20

Step 7: (10x ÷ 10) = (20 ÷ 10)

Step 8: x = 20/10

Step 9: x = 20/10 = 2

Step 10: x = 2

Answer 2

Remark

Sometimes you can avoid the distributive property. This is one of those cases. Start by dividing by 5. You can only do this is there a common factor between the left and right sides of the equal sign.

Solve

There is only 1 solution. If there was an x^2 somewhere, you would have 2 and if there was an x^3 there would be 3.

5(2x - 3) = 5 Divide both sides by 5

5(2x - 3)/5 = 5/5

(2x - 3) = 1 Remove the brackets.

2x - 3 = 1 Add 3 to both sides.

2x = 1 + 3

2x = 4 Divide by 2

x = 4/2

x = 2 <<<<< Answer