Question

Which of the equations below have one solution? Select all that apply. 8x–3x+5=5x–2 9=3(5x–2) 6x–(3x+8)=16 9x+4–x=4(2x+1)

Answer 1

The equations that have one solution are 9=3(5x–2) and 6x–(3x+8)=16

Explanation:

To determine which equations have one solution, we will determine the solution(s) to all the equations (that is, find the value of the unknown, x).

1. 8x–3x+5=5x–2

This becomes

5x+5=5x-2

Subtract 5x from both sides

5x-5x+5 = 5x-5x-2

0+5 = 0-2

This equation has no solution

2. 9=3(5x–2)

First, open the bracket by distributing 3

∴ 9 = 15x - 6

Then, add 6 to both sides

9+6 = 15x -6 +6

15 = 15x

Divide both sides by 15

15/15 = 15x/15

1 = x

∴ x = 1

This has one solution.

3. 6x–(3x+8)=16

Open the bracket by distributing –1

6x -3x -8 = 16

3x - 8 = 16

Add 8 to both sides

3x -8 +8 = 16 + 8

3x = 24

Divide both sides by 3

3x/3 = 24/3

x = 8

This has one solution.

4. 9x+4–x=4(2x+1)

This becomes

9x -x +4 = 4(2x+1)

Then, 8x +4 = 4(2x+1)

Open the bracket by distributing 4

8x +4 = 8x +4

This is true for any value of x.

Hence, the equations that have one solution are 9=3(5x–2) and 6x–(3x+8)=16.