Question

solve each inequality below. graph the solution on a number line.

1. 2x - 3 < 5
2. -4(x - 3) ≤ 20
3. a cargo elevator has a maximum carrying capacity of 400 pounds.

a. if each cargo box weighs 25 pounds, what is the maximum number of cargo boxes that the elevator can hold?
b. a 150 - pound person rides in the elevator with the cargo boxes. what is the maximum number of cargo boxes that the person can take with them in the elevator?

Explanation:

8. Solve the inequality $2x - 3<5$ and graph the solution

Step1: Add 3 to both sides

$2x-3 + 3<5 + 3$
$2x<8$

Step2: Divide both sides by 2

$\frac{2x}{2}<\frac{8}{2}$
$x < 4$
To graph, draw an open - circle at 4 on the number line (since $x$ is less than 4, not equal to 4) and shade the line to the left of 4.

9. Solve the inequality $-4(x - 3)\leq20$ and graph the solution

Step1: Distribute - 4

$-4x+12\leq20$

Step2: Subtract 12 from both sides

$-4x+12 - 12\leq20 - 12$
$-4x\leq8$

Step3: Divide both sides by - 4 and reverse the inequality sign

$\frac{-4x}{-4}\geq\frac{8}{-4}$
$x\geq - 2$
To graph, draw a closed - circle at - 2 on the number line (since $x$ can be equal to - 2) and shade the line to the right of - 2.

10a. A cargo elevator has a maximum carrying capacity of 400 pounds. If each cargo box weighs 25 pounds, find the maximum number of cargo boxes the elevator can hold

Step1: Let the number of boxes be $n$. Set up an equation based on weight

$25n\leq400$

Step2: Divide both sides by 25

$\frac{25n}{25}\leq\frac{400}{25}$
$n\leq16$
The maximum number of cargo boxes is 16.

10b. A 150 - pound person rides in the elevator with the cargo boxes. Find the maximum number of cargo boxes the person can take

Answer:

1. Solution: $x < 4$, Graph: Open - circle at 4, shade left.
2. Solution: $x\geq - 2$, Graph: Closed - circle at - 2, shade right.

10a. 16
10b. 10