To determine the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\(\frac{3}{4} x + 4 = 7\)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
\frac{3}{4} x + 4 = 7
\][/tex]
2. Isolate the term with [tex]\( x \)[/tex]:
Subtract 4 from both sides of the equation to get:
[tex]\[
\frac{3}{4} x = 7 - 4
\][/tex]
3. Simplify the right-hand side:
[tex]\[
\frac{3}{4} x = 3
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{4}\)[/tex], which is [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
x = 3 \cdot \frac{4}{3}
\][/tex]
5. Simplify the multiplication:
[tex]\[
x = 4
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the equation [tex]\(\frac{3}{4} x + 4 = 7\)[/tex] true is [tex]\( 4 \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
