Which equation has exactly ONE solution?
A 8+3x/2=13+x
B 3+12x/2=6x+15
C 10+15x/5 =3x+10
D 4x−20/4= x − 5
To determine which equation has exactly one solution, we need to solve each equation and see how many solutions it has.
Let's go through each equation:
A) 8+3x/2=13+x
To solve for x, we can start by isolating x on one side:
3x/2 - x = 13 - 8
Multiplying through by 2 eliminates the fraction:
3x - 2x = 10
x = 10
B) 3+12x/2=6x+15
Again, let's isolate x on one side:
12x/2 - 6x = 15 - 3
6x - 6x = 12
0 ≠ 12
C) 10+15x/5 =3x+10
Isolating x on one side:
15x/5 - 3x = 10 - 10
12x/5 = 0
12x = 0
x = 0
D) 4x−20/4 = x − 5
Let's isolate x on one side:
4x - 20/4 = x - 5
Multiplying through by 4 to eliminate the fraction:
16x - 20 = 4x - 20
16x - 4x = 20 - 20
12x = 0
x = 0
Out of the four equations, only equation A has exactly one solution, which is x = 10.
Therefore, the answer is A) 8+3x/2=13+x.