Question

Solve for xx.

-15x + 4 ≤ 109 OR -6x + 70 > -2
Choose 1 answer:


(Choice A)
A
x≥−7

(Choice B)
B
-7≤x<12

(Choice C)
C
x<12
(Choice D)
D
There are no solutions

(Choice E)
E
All values of x are solutions

Answer 1

E. All values of x are solutions

Explanation:

• -15x + 4 ≤ 109
• -6x + 70 > -2

Solve for x in the first equation. Subtract 4 from both sides.

-15x ≤ 105

Divide both sides by -15. Since this is a negative number the sign will flip.

x ≥ -7

Solve for x in the second equation. Subtract 70 from both sides.

-6x > -72

Divide both sides by -6; the sign flips.

x < 12

Since this is an OR problem we won't be combining the two solutions for x. Therefore you would graph x ≥ -7 and x < 12 separately.

The graph would look like this: (image attached)

Since the two lines cross pathways to cover the entire number line, this means that there are infinite values of x.

The answer should be E.

Answer 2

E All values of x are solutions

Explanation:

-15x + 4 ≤ 109 OR -6x + 70 > -2

We will solve the left inequality first

-15x + 4 ≤ 109

Subtract 4 from each side

-15x +4-4 ≤ 109 -4

-15x ≤ 105

Divide by -15 Remember to flip the inequality

-15x/-15 ≥ 105/-15

x ≥-7

Now we solve the right side

-6x + 70 > -2

Subtract 70 from each side

-6x + 70 -70> -2-70

-6x> -72

Divide by -6 Remember to flip the inequality

-6x/-6< -72/-6

x < 12

Since this is an OR

x ≥-7 OR x < 12

This covers the entire number line

x is all real numbers