Question

1. solve the following inequality: 3(2x + 4) < 30

14a solve the inequality.
x < 3
14b 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 $6x<18$.

Step3: Divide both sides by 6

$\frac{6x}{6}<\frac{18}{6}$, resulting in $x < 3$.

For 14b:

On the number line, draw an open circle at 3 (since $x$ is less than 3, not less than or equal to 3) and shade the line to the left of 3.

Answer:

14a: $x < 3$
14b: Draw an open circle at 3 and shade the line to the left of 3 on the number - line.