Question

Which number line represents the solution to the inequality below?
-2x + 5 > 15

A.

-11-10-9-8-7-6-5-4-3-2-101
B.

-13-12-11-10-9-8-7-6-5-4-3-2-1
C.

-10-9-8-7-6-5-4-3-2-1012
D.

-13-12-11-10-9-8-7-6-5-4-3-2-1

Answer 1

To solve the inequality \(-2x + 5 > 15\), we will first isolate \(x\).

1. Subtract 5 from both sides:
\[
-2x > 15 - 5
\]
\[
-2x > 10
\]

2. Divide both sides by -2. Remember that when dividing by a negative number, the inequality sign flips:
\[
x < \frac{10}{-2}
\]
\[
x < -5
\]

Now we know that the solution to the inequality is \(x < -5\).

Next, we look for which number line illustrates this solution. In a number line, values that are less than -5 will be represented by an open circle at -5 (indicating -5 itself is not included) and shading to the left of -5.

Looking at the options:

**A.** Does not have indication of values less than -5.

**B.** Does not have indication of values less than -5.

**C.** Does not have indication of values less than -5.

**D.** Does not have indication of values less than -5.

None of the provided options contain a number line showing the solution \(x < -5\) correctly.