Question

solve and graph the following inequality: 10 + 8x ≥ 2 + 3x

Explanation:

Step1: Subtract 3x from both sides

$10 + 8x-3x\geq2 + 3x-3x$
$10 + 5x\geq2$

Step2: Subtract 10 from both sides

$10 + 5x-10\geq2-10$
$5x\geq - 8$

Step3: Divide both sides by 5

$\frac{5x}{5}\geq\frac{-8}{5}$
$x\geq-\frac{8}{5}$

To graph: On a number - line, put a closed circle at $x =-\frac{8}{5}=-1.6$ (since the inequality is $\geq$) and shade to the right.

Answer:

Inequality: $x\geq-\frac{8}{5}$; Graph: Closed circle at $x = - 1.6$ and shade to the right on the number - line.