Question

Solve the equation.
12 left parenthesis 2 x minus 5 right parenthesis equals 4 left parenthesis 6 x plus 3 right parenthesis
Question content area bottom
Part 1
A.
0
B.72
72
C.
All real numbers
D.
No solution

Answer 1

Let's solve the equation step by step:

Given:
\[ 12(2x - 5) = 4(6x + 3) \]

1. Distribute both sides:
\[
12 \cdot 2x - 12 \cdot 5 = 4 \cdot 6x + 4 \cdot 3
\]
This simplifies to:
\[
24x - 60 = 24x + 12
\]

2. Next, we will subtract \( 24x \) from both sides:
\[
24x - 60 - 24x = 24x + 12 - 24x
\]
This simplifies to:
\[
-60 = 12
\]

This statement \(-60 = 12\) is false; therefore, there is no value of \( x \) that can satisfy the equation.

The conclusion is:
**D. No solution**.