Question

example 3
solve each inequality. then graph the solution on a number line.

1. $-3(7n + 3) < 6n$
2. $21 \geq 3(o - 7) + 9$
3. $2y + 4 > 2(3 + y)$
4. $3(2 - b) < 10 - 3(b - 6)$
5. $7 + t \leq 2(t + 3) + 2$
6. $8a + 2(1 - 5a) \leq 20$

Explanation:

Problem 16: $-3(7n + 3) < 6n$

Step1: Distribute the -3

$-21n - 9 < 6n$

Step2: Add 21n to both sides

$-9 < 27n$

Step3: Divide both sides by 27

$-\frac{1}{3} < n$ or $n > -\frac{1}{3}$

Step1: Distribute the 3

$21 \geq 3o - 21 + 9$

Step2: Simplify the right side

$21 \geq 3o - 12$

Step3: Add 12 to both sides

$33 \geq 3o$

Step4: Divide both sides by 3

$11 \geq o$ or $o \leq 11$

Step1: Distribute the 2

$2y + 4 > 6 + 2y$

Step2: Subtract 2y from both sides

$4 > 6$
This is a contradiction, so there is no solution.

Answer:

$n > -\frac{1}{3}$

Problem 17: $21 \geq 3(o - 7) + 9$