Question

Solve the equation.
24 left parenthesis x plus 1 right parenthesis equals 6 left parenthesis 4 x minus 5 right parenthesis plus 54
Question content area bottom
Part 1
A.
No solution
B.24
24
C.
0
D.
All real numbers

Answer 1

To solve the equation \( 24(x + 1) = 6(4x - 5) + 54 \), we'll start by expanding both sides.

1. Expand both sides:
\[
24(x + 1) = 24x + 24
\]
\[
6(4x - 5) + 54 = 24x - 30 + 54 = 24x + 24
\]

2. Now the equation looks like this:
\[
24x + 24 = 24x + 24
\]

3. To see if this equation is true for all \( x \), we can subtract \( 24x \) from both sides:
\[
24 = 24
\]

Since \( 24 = 24 \) is always true, this indicates that the equation is satisfied for all values of \( x \).

Thus, the solution is:

**D. All real numbers**.