Question

1. Storing milk at temperatures colder than 35°F can affect its quality of taste. However, storing milk at temperatures warmer than 40°F is an unsafe food practice.

Which of the inequalities below represent the union of these improper storage temperatures, t, in degrees Fahrenheit?

A. t > 35 or t <40
B. t < 35 or t >40
C. t > 35 AND t < 40
D. t < 35 AND t > 40

2. What are the solution(s) to the absolute value equation below?
15| x-7|+4=10|x-7|+4
A. x= - 5\7 or x = 5\7
B. x=5 or x= -5
C. only x=7
D. x= 7/5 or x= -7\5

3. Match the absolute value equation with the statement that describes the solutions to that equation.

A. two solutions

B. solution

C. no solution

|x+1|+5=2
|4x+12|=0
|3x|=9

Answer 1

1.

Storing milk at temperatures smaller than 35°F can affect its quality of taste.

hence t > 35°F

storing milk at temperatures greater than 40°F is an unsafe food practice. hence

t < 40°F

so correct choice is

C. t > 35 AND t < 40

2.

15| x-7|+4=10|x-7|+4

subtracting 4 both side

15| x-7|+4- 4 =10|x-7|+4 - 4

15| x-7| = 10|x-7|

this is possible when |x-7| = 0

hence x - 7 = 0

x = 7

hence correct choice is

C. only x=7

3.

|x+1|+5=2

we know that , |x+1| ≥ 0

adding 5 both side

|x+1| + 5 ≥ 0 + 5

|x+1| + 5 ≥ 5

hence the relation |x+1|+5=2 is false.

C. no solution

|4x+12|=0

4x+12 = 0

x = -12/4

x = - 3

hence B. solution

|3x|=9

3x =
`\pm`9

x =
`\pm`9/3

x =
`\pm`3

hence

A. two solutions