Question

$$\frac { 1 } { 2 } ( 6 a - 4 ) leq 7$$

Explanation:

Step1: Expand the inequality

Multiply out the left - hand side: $\frac{1}{2}(6a - 8)=3a-4$. So the inequality becomes $3a - 4\leq7$.

Step2: Add 4 to both sides

To isolate the term with \(a\), add 4 to both sides of the inequality: $3a-4 + 4\leq7 + 4$, which simplifies to $3a\leq11$.

Step3: Divide by 3

Divide both sides by 3: $a\leq\frac{11}{3}\approx3.67$.

Answer:

The second number line (with a closed circle at \(-3\) and the line extending to the right) is incorrect. The correct solution of the inequality $\frac{1}{2}(6a - 8)\leq7$ is $a\leq3$, so the number line with a closed circle at \(3\) and the line extending to the left is the correct representation.