To solve the equation \(4x + 7 = 23 - 8\), we first simplify the right side of the equation:
\[ 23 - 8 = 15 \]
Now the equation becomes:
\[ 4x + 7 = 15 \]
Next, we isolate the term with \(x\) by subtracting 7 from both sides:
\[ 4x = 15 - 7 \]
Calculating the right side:
\[ 15 - 7 = 8 \]
Now we have:
\[ 4x = 8 \]
To solve for \(x\), we divide both sides by 4:
\[ x = \frac{8}{4} = 2 \]
Thus, the solution is:
\[ x = 2 \]