Question

1. solve the basic equation and graph its solution set on the number line: $x - 2geq - 9$
2. solve the basic equation and graph its solution set on the number line: $8 + x> - 1$

Explanation:

Step1: Solve the first inequality

Add 2 to both sides of $x - 2\geq - 9$.
$x-2 + 2\geq - 9+2$
$x\geq - 7$
To graph it on the number - line, draw a closed circle at - 7 (because the inequality is $\geq$) and shade to the right.

Step2: Solve the second inequality

Subtract 8 from both sides of $8 + x> - 1$.
$8+x-8>-1 - 8$
$x>-9$
To graph it on the number - line, draw an open circle at - 9 (because the inequality is $>$) and shade to the right.

Answer:

For $x - 2\geq - 9$, the solution is $x\geq - 7$ and its graph has a closed circle at - 7 and shading to the right. For $8 + x> - 1$, the solution is $x>-9$ and its graph has an open circle at - 9 and shading to the right.