Question

solve each inequality and then graph your solution.

1. $-7x \geq 35$
2. $x - 16 < 11$
3. $8 \geq x + 10$

the number line below represents the solution set to which inequality? shade the correct card

Explanation:

Step1: Isolate x, divide by -7 (flip inequality)

$\frac{-7x}{-7} \leq \frac{35}{-7}$

Step2: Simplify to get solution for Q7

$x \leq -5$

Step3: Isolate x, add 16 to both sides

$x - 16 + 16 < 11 + 16$

Step4: Simplify to get solution for Q8

$x < 27$

Step5: Isolate x, subtract 10 from both sides

$8 - 10 \geq x + 10 - 10$

Step6: Simplify to get solution for Q9

$-2 \geq x$ or $x \leq -2$

Answer:

1. For $-7x \geq 35$: $x \leq -5$

(Graph: Closed dot at -5, shade left on the number line)

1. For $x - 16 < 11$: $x < 27$

(Graph: Open dot at 27, shade left on the number line)

1. For $8 \geq x + 10$: $x \leq -2$

(Graph: Closed dot at -2, shade left on the number line)