Question

9

Select the correct answer.
Which statement is true about this equation?
-9(x + 3) + 12 = -3(2x + 5) - 3x
OA
The equation has one solution, x= 1.
OB. The equation has one solution, x = 0.
OC. The equation has no solution.
OD
The equation has infinitely many solutions.
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Answer 1

Answer: D. The equation has infinitely many solutions.

Explanation:

Given equation:
`-9(x + 3) + 12 = -3(2x + 5) - 3x`

`\Rightarrow -9(x)+(-9)(3)+12=(-3)(2x)+(-3)(5)-3x\\\\\Rightarrow\ -9x-27+12=-6x-15-3x\\\\\Rightarrow\ -9x-15=-9x-15\\\\\Rightarrow\ -9x+9x=-15+15\\\\\Rightarrow\ 0=0`

which is true.

This happens when all numbers are solutions.

i.e. The equation has infinitely many solutions.

Correct option : D.