If 5(3x+ 4)−8(6x+ 7)=9x−8, then what is the value of (3x+ 4) ?

The correct answer is 2.

Step 1: Simplify the given equation to solve for x

We are given the linear equation:

$5(3x+4)-8(6x+7)=9x-8$

First, expand the terms on the left-hand side using the distributive property:

$15x+20-48x-56=9x-8$

Combine like terms on the left side:

$-33x-36=9x-8$

Step 2: Isolate x

Rearrange the terms by bringing all terms with $x$ to the left side and constant terms to the right side:

$-33x-9x=-8+36$

$-42x=28$

Divide both sides by -42:

$x=\frac{28}{-42}=-\frac{2}{3}$

Step 3: Calculate the value of (3x + 4)

Substitute $x=-\frac{2}{3}$ into the expression $3x+4$:

$3x+4=3\left(-\frac{2}{3}\right)+4$

$3x+4=-2+4=2$

Thus, the value of $(3x+4)$ is 2.