Answer:
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.