what is the solution to the equation $sqrt3{5x - 4}=sqrt3{7x + 8}$?\n$x=-6$\n$x = - 1$\n$x = 1$\n$x = 2$

Explanation:

Step1: Cube both sides of the equation

Since $\sqrt[3]{a}=\sqrt[3]{b}$ implies $a = b$, we have $5x - 4=7x + 8$.

Step2: Isolate the variable terms

Subtract $5x$ from both sides: $-4=7x - 5x+8$, which simplifies to $-4 = 2x+8$.

Step3: Solve for $x$

Subtract 8 from both sides: $-4-8=2x$, so $-12 = 2x$. Then divide both sides by 2: $x=\frac{-12}{2}=-6$.

Answer:

A. $x = - 6$