Question

solve the inequality and graph the solution. 5x - 8x ≥ 3x + 8. choose the correct graph below.

Explanation:

Step1: Combine like - terms on left side

$5x−8x=-3x$, so the inequality becomes $-3x\geq3x + 8$.

Step2: Subtract $3x$ from both sides

$-3x-3x\geq3x + 8-3x$, which simplifies to $-6x\geq8$.

Step3: Divide both sides by $-6$ and reverse the inequality sign

$x\leq\frac{8}{-6}=-\frac{4}{3}$ (when dividing an inequality by a negative number, the direction of the inequality sign changes).

Answer:

The solution of the inequality is $x\leq-\frac{4}{3}$. The correct graph is A (since it has a closed - circle at $-\frac{4}{3}$ and the arrow points to the left, indicating all values less than or equal to $-\frac{4}{3}$).