Question

1. $5k - 2k > -9$
2. $30 - 6a < -3(5 + 7a)$

Explanation:

Step1: Combine like terms

$5k - 2k = 3k$, so $3k > -9$

Step2: Isolate $k$

Divide both sides by 3: $\frac{3k}{3} > \frac{-9}{3}$

Step3: Simplify to find $k$

$k > -3$

Step4: Expand right-hand side

$-3(5+7a) = -15 -21a$, so $30 -6a < -15 -21a$

Step5: Move $a$ terms to left

Add $21a$ to both sides: $30 +15a < -15$

Step6: Isolate $a$ term

Subtract 30 from both sides: $15a < -15 -30$

Step7: Simplify right-hand side

$15a < -45$

Step8: Solve for $a$

Divide by 15: $\frac{15a}{15} < \frac{-45}{15}$ → $a < -3$

Answer:

1. For $5k - 2k > -9$: $k > -3$

(On the number line, draw an open circle at $-3$ and shade to the right.)

1. For $30 - 6a < -3(5 + 7a)$: $a < -3$

(On the number line, draw an open circle at $-3$ and shade to the left.)