Question

solve each problem. show all your work!

1. the temperature at noon on a summer day was 88°c. at midnight, the temperature had dropped 12°. what was the temperature at midnight?
2. a group of hikers is descending a mountain at a rate of 400 feet per hour. after 3 hours, what integer represents their total change in elevation?

use the distributive property to simplify each expression.

1. 4(x + 3)
2. 5(3x - 6)
3. -2(7x + 8)

Explanation:

Step1: Subtract temp drop from noon temp

$88 - 12 = 76$

Step2: Multiply rate by time for elevation change

$400 \times 3 = 1200$, descending means $-1200$

Step3: Distribute 4 to terms in parentheses

$4(x + 3) = 4x + 4\times3 = 4x + 12$

Step4: Distribute 5 to terms in parentheses

$5(3x - 6) = 5\times3x - 5\times6 = 15x - 30$

Step5: Distribute -2 to terms in parentheses

$-2(7x + 8) = -2\times7x + (-2)\times8 = -14x - 16$

Answer:

1. $76^\circ\text{C}$
2. $-1200$
3. $4x + 12$
4. $15x - 30$
5. $-14x - 16$