Question

Match each inequality to the number line that represents its solution

Answer 1

Answer:

Part 1)  shaded area at left of x=8 (close circle) ---> $-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}$  

Part 2) shaded area at left of x=-5 (close circle) ---> $-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}$

Part 3) shaded area at left of x=-6 (close circle) ---> $\frac{3x}{2}+105 \leq 96$

Part 4) shaded area at left of x=7 (close circle) ---> $-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}$

see the attached figure

Step-by-step explanation:

Part 1) we have

$-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}$  

Multiply by -10 both sides

$x-2 \leq 6$

Adds 2 both sides

$x \leq 6+2$

$x \leq 8$

The solution is the interval -----> (-∞,8]

All real numbers less than or equal to 8

In a number line the solution is the shaded area at left of x=8 (close circle)

Part 2) we have

$-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}$

Multiply by -6 both sides

$100x+11 \leq -489$

Subtract 11 both sides

$100x \leq -489-11$

$100x \leq -500$

Divide by 100 both sides

$x \leq -5$

The solution is the interval -----> (-∞,-5]

All real numbers less than or equal to -5

In a number line the solution is the shaded area at left of x=-5 (close circle)

Part 3) we have

$\frac{3x}{2}+105 \leq 96$

Multiply by 2 both sides

$3x+210 \leq 192$

Subtract 210 both sides

$3x \leq 192-210$

$3x \leq -18$

Divide by 3 both sides

$x \leq -18/3$

$x \leq -6$

The solution is the interval -----> (-∞,-6]

All real numbers less than or equal to -6

In a number line the solution is the shaded area at left of x=-6 (close circle)

Part 4) we have

$-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}$

Multiply by -18 both sides

$13x-10 \leq 81$

Adds 10 both sides

$13x \leq 91$

Divide by 13 both sides

$x \leq 91/13$

$x \leq 7$

The solution is the interval -----> (-∞,7]

All real numbers less than or equal to 7

In a number line the solution is the shaded area at left of x=7 (close circle)