Question

solve ( 35 < 7(2 - b) ) or ( \frac{1}{3}(15b - 12) geq 21 ).
solution: ( square ) or ( square )
graph the solution.
number line and graphing options omitted

Explanation:

Step1: Solve first inequality

Start with $35 < 7(2 - b)$. Divide both sides by 7:
$\frac{35}{7} < \frac{7(2 - b)}{7}$
$5 < 2 - b$
Subtract 2 from both sides:
$5 - 2 < -b$
$3 < -b$
Multiply by -1 (reverse inequality):
$b < -3$

Step2: Solve second inequality

Start with $\frac{1}{3}(15b - 12) \geq 21$. Multiply both sides by 3:
$15b - 12 \geq 21 \times 3$
$15b - 12 \geq 63$
Add 12 to both sides:
$15b \geq 63 + 12$
$15b \geq 75$
Divide by 15:
$b \geq \frac{75}{15}$
$b \geq 5$

Answer:

$b < -3$ or $b \geq 5$

For the graph:

• For $b < -3$: Draw an open circle at $-3$ on the number line, with an arrow pointing left.
• For $b \geq 5$: Draw a closed circle at $5$ on the number line, with an arrow pointing right.