Question

1. consider the inequality: 3(2x + 4) > -30.

13a solve the inequality.
x > -7
13b now, plot the inequality 3(2x + 4) > -30 on the number line below.

Explanation:

Step1: Expand the left - hand side

$3(2x + 4)=6x+12$, so the inequality becomes $6x + 12>-30$.

Step2: Subtract 12 from both sides

$6x+12 - 12>-30 - 12$, which simplifies to $6x>-42$.

Step3: Divide both sides by 6

$\frac{6x}{6}>\frac{-42}{6}$, resulting in $x > - 7$.

For 13b:
On the number - line, draw an open circle at $x=-7$ (since the inequality is $x > - 7$ and $-7$ is not included) and draw an arrow to the right of $-7$ to represent all the values of $x$ that satisfy the inequality.

Answer:

13a: $x > - 7$
13b: Draw an open circle at $-7$ on the number - line and an arrow to the right of $-7$.