question\nsolve for x in simplest form.\n6 = \\frac{4}{3}(8x + 9)

Explanation:

Step1: Distribute the fraction

Multiply $\frac{4}{3}$ by each term inside the parentheses. $6=\frac{4}{3}\times8x+\frac{4}{3}\times9$ $6=\frac{32}{3}x + 12$

Step2: Isolate the term with x

Subtract 12 from both sides. $6 - 12=\frac{32}{3}x+12 - 12$ $- 6=\frac{32}{3}x$

Step3: Solve for x

Multiply both sides by the reciprocal of $\frac{32}{3}$, which is $\frac{3}{32}$. $-6\times\frac{3}{32}=\frac{32}{3}x\times\frac{3}{32}$ $x=-\frac{18}{32}=-\frac{9}{16}$

Answer:

$x =-\frac{9}{16}$