Question

I need help on this math problem:

Solve for X.
11x + 4 < 15 OR 12x − 7 > −25
A: -3/2 < x < 1
B: x > -3/2
C: x < 1
D: There are NO solutions.
E: All values of X are solutions.

Answer 1

E

Step-by-step explanation:

11x-4<15

11x<11

x<1

12x-7>-25

12x>-18

x>-3/2

x<1 or x>-3/2, that covers the whole x-axis domain

Answer 2

Answer: Choice E

All values of x are solutions

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Step-by-step explanation:

Let's solve the first inequality for x

11x + 4 < 15

11x < 15-4

11x < 11

x < 11/11

x < 1

In the second step I subtracted 4 from both sides to undo the "plus 4". Then a bit later on, I divided both sides by 11 to fully isolate x. The inequality sign doesn't flip since we didn't divide both sides by a negative number.

The graph of x < 1 involves an open hole at 1 on the number line. The shading is to the left.

See the diagram below. Specifically, refer to the red portion of the diagram.

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Next, we solve the other inequality

12x - 7 > -25

12x > -25+7

12x > -18

x > -18/12

x > -3/2

The graph will have an open hole at -3/2 = -1.5 and shading to the right. This is the blue portion of the graph shown below.

Notice how the two intervals, when combined together, span the entire number line. We can pick any number we want and it will satisfy one or both of these inequalities.

Therefore, All values of x are solutions (choice E)

Side note: if we changed that "OR" to "AND", then choice E would not be the answer. Instead, it would be choice A. This is because the two intervals overlap to form this restricted compound inequality.