Question

Which number line represents the solution to the inequality below?

2x + 5 > 9
A.

-101234567891011
B.

0123456789101112
C.

-3-2-10123456789
D.

-101234567891011

Answer 1

To solve the inequality \( 2x + 5 > 9 \), we start by isolating \( x \).

1. Subtract 5 from both sides:
\[
2x > 9 - 5
\]
This simplifies to:
\[
2x > 4
\]

2. Divide both sides by 2:
\[
x > \frac{4}{2}
\]
This further simplifies to:
\[
x > 2
\]

Now we need to represent the solution \( x > 2 \) on a number line. This means we need a number line that has an open circle at 2 (indicating that 2 is not included in the solution) and will extend to the right (indicating that all numbers greater than 2 satisfy the inequality).

Among the options provided:
- **Option A:** -101234567891011 (does not show 2 clearly, not a clear representation)
- **Option B:** 0123456789101112 (correctly shows open circle at 2 and extends to the right)
- **Option C:** -3-2-10123456789 (does not include 2 at all)
- **Option D:** -101234567891011 (same as option A)

The correct representation of the solution \( x > 2 \) is **Option B**.