Question

1. solve -2x + 10 < 12 for x and graph it on the number line below. -10 -5 0 5 10 interval notation ____________

Explanation:

Step1: Subtract 10 from both sides

$-2x+10 - 10<12 - 10$
$-2x<2$

Step2: Divide both sides by - 2 and reverse the inequality sign

$\frac{-2x}{-2}>\frac{2}{-2}$ (When dividing by a negative number, the inequality sign flips)
$x > - 1$

To graph on the number - line: Draw an open circle at - 1 (because the inequality is $x>-1$, not $x\geq - 1$) and draw an arrow to the right.

In interval notation, the solution is $(-1,\infty)$.

Answer:

The solution of the inequality is $x > - 1$. The graph has an open circle at - 1 and an arrow to the right. The interval notation is $(-1,\infty)$.