Question

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solve each inequality and graph the solution set on the number line.

1. $16 \leq 3x + 4$

solution:

1. $- 37 < 7x - 2$

solution:

Explanation:

For problem 17: $16 \leq 3x + 4$

Step1: Subtract 4 from both sides

$16 - 4 \leq 3x + 4 - 4$
$12 \leq 3x$

Step2: Divide by 3 on both sides

$\frac{12}{3} \leq \frac{3x}{3}$
$4 \leq x$ or $x \geq 4$

Step3: Graph setup

On the number line, draw a closed circle at 4, then shade all values to the right (towards 10).

For problem 18: $-37 < 7x - 2$

Step1: Add 2 to both sides

$-37 + 2 < 7x - 2 + 2$
$-35 < 7x$

Step2: Divide by 7 on both sides

$\frac{-35}{7} < \frac{7x}{7}$
$-5 < x$ or $x > -5$

Step3: Graph setup

On the number line, draw an open circle at -5, then shade all values to the right (towards 10).

Answer:

1. For $16 \leq 3x + 4$, the solution is $x \geq 4$. (Graph: closed circle at 4, shade right)
2. For $-37 < 7x - 2$, the solution is $x > -5$. (Graph: open circle at -5, shade right)