Answer:
We conclude that 10x + 2 = (10 + 2)x has only 1 solution.
Hence, option (D) is correct.
Explanation:
A.
10x + 2x = (10 + 2)x - 2
Checking the equation in Part A
10x + 2x = (10 + 2)x - 2
10x + 2x = 10x+2x-2
10x + 2x - 10x - 2x = -2
0 = -2
The sides are not equal.
Hence, NO SOLUTION!
B.
10x + 2 = (10 + 2)x - 2x
Checking the equation in Part B
10x + 2 = 10x+2x - 2x
10x + 2 - 10x - 2x + 2x = 0
2 = 0
The sides are not equal.
Hence, NO SOLUTION!
C.
10x + 2x = (10 + 2)x
Checking the equation in Part C
10x + 2x = 10x+2x
10x + 2x - 10x - 2x = 0
0 = 0
Both sides are equal.
It is true for all x.
D.
10x + 2 = (10 + 2)x
Checking the equation in Part D
10x + 2 = 10x+2x
10x - 10x - 2x = -2
-2x = -2
Divide both sides by -2
x = 1
Hence, 10x + 2 = (10 + 2)x has only 1 solution.
Therefore, we conclude that 10x + 2 = (10 + 2)x has only 1 solution.
Hence, option (D) is correct.