Question

$\frac{4}{5}(x - 2) \leq 6$

Explanation:

Step1: Eliminate the fraction

Multiply both sides by 5:
$$5\times\frac{4}{5}(x-2) \leq 6\times5$$
$$4(x-2) \leq 30$$

Step2: Expand the left side

Distribute the 4:
$$4x - 8 \leq 30$$

Step3: Isolate the variable term

Add 8 to both sides:
$$4x \leq 30 + 8$$
$$4x \leq 38$$

Step4: Solve for x

Divide both sides by 4:
$$x \leq \frac{38}{4}$$
$$x \leq \frac{19}{2}$$
$$x \leq 9.5$$

Step5: Graph on number line

Draw a closed circle at 9.5, shade all values to the left (since $x$ is less than or equal to 9.5).

Answer:

$x \leq 9.5$ (or $x \leq \frac{19}{2}$); on the number line, mark a closed dot at 9.5 and shade the region to the left of this point.