Question

Can you please solve and explain how

Answer 1

$36+3(4x-9)=c(2x+1)+25\\\\36+12x-27=2cx+c+25\\\\9+12x=2cx+c+25\ \ \ |-9\\\\12x=2cx+c+16\ \ \ |-2cx\\\\12x-2cx=c+16$

The equation has no solution. Therefore, x must be eliminated. Then the equation will not make sense if the left side is not equal to the right side (different numbers).

$12x-2cx=0\to 12-2c=0\to c=6$

Substitute the value of c to the equation and check it:

$12x-2(6)x=6+16\\\\12x-12x=22\\\\0=22\ FALSE$

Answer: C) 6

Answer 2

First, it would help to simplify each side more:

Left side: 36 + 3(4x - 9) = 36 + 12x - 27 = 12x + 9

Right side: c(2x + 1) + 25 = 2cx + c + 25

Write the simplified equation:

12x + 9 = 2cx + c + 25

Usually when there is no solution, the coefficients of the variable on both sides are the same, so we can make the coefficient if x on the right side into 12:

2cx >>> 12x

Then, c must equal 6 to make this true.

The answer is choice (C).