Question

an inequality is shown. 2(3x - 4)≥4x + 8. solve the inequality and graph the solution on the number line.

Explanation:

Step1: Expand the left - hand side

$2(3x - 4)=6x-8$, so the inequality becomes $6x - 8\geq4x + 8$.

Step2: Move the terms with $x$ to one side

Subtract $4x$ from both sides: $6x-4x - 8\geq4x-4x + 8$, which simplifies to $2x-8\geq8$.

Step3: Move the constant term to the other side

Add 8 to both sides: $2x-8 + 8\geq8 + 8$, resulting in $2x\geq16$.

Step4: Solve for $x$

Divide both sides by 2: $\frac{2x}{2}\geq\frac{16}{2}$, so $x\geq8$.

To graph on the number - line, we draw a closed circle at 8 (because the inequality is $\geq$) and draw an arrow to the right.

Answer:

$x\geq8$, and on the number - line, a closed circle at 8 and an arrow to the right.