Question

1. solve the basic equation and graph its solution set on the number line: 12 + x ≤ 5
2. solve the basic equation and graph its solution set on the number line: - 8x < 48

Explanation:

Step1: Solve the first inequality

Subtract 12 from both sides of $12 + x\leq5$.
$12 + x-12\leq5 - 12$
$x\leq - 7$

Step2: Graph the first - inequality solution

On the number - line, draw a closed circle at - 7 (because the inequality is $\leq$) and shade to the left.

Step3: Solve the second inequality

Divide both sides of $-8x\lt48$ by - 8. When dividing an inequality by a negative number, the direction of the inequality sign changes.
$\frac{-8x}{-8}>\frac{48}{-8}$
$x > - 6$

Step4: Graph the second - inequality solution

On the number - line, draw an open circle at - 6 (because the inequality is $>$) and shade to the right.

Answer:

For $12 + x\leq5$, the solution is $x\leq - 7$ and the graph has a closed circle at - 7 and shading to the left.
For $-8x\lt48$, the solution is $x > - 6$ and the graph has an open circle at - 6 and shading to the right.