Question

Which graph shows the solution to the inequality below?

6<−2x

A.
The number line shows numbers from -18 to 6. There is an open circle at -12, a bold line from -12 heading leftwards.


B.
The number line shows numbers from -18 to 6. There is an open circle at -3, a bold line from -3 heading leftwards.


C.
The number line shows numbers from -18 to 6. There is an open circle at -3, a bold line from -3 heading rightwards.


D.
The number line shows numbers from -18 to 6. There is an open circle at -12, a bold line from -12 heading rightwards.

Answer 1

To solve the inequality \( 6 < -2x \), we first rearrange it to isolate \( x \).

1. Subtract 6 from both sides:
\[
0 < -2x - 6
\]
or equivalently,
\[
-2x > -6
\]

2. Now, divide both sides by -2. Remember that when we divide by a negative number, the direction of the inequality flips:
\[
x < 3
\]

This means that the solution to the inequality is all numbers less than 3.

Now, we need to find the correct graph representation of this inequality. The solution indicates an open circle at 3 (because it does not include 3 itself) and a bold line extending leftwards from that point to indicate values less than 3.

Now, let's examine the options:
- **A**: Open circle at -12, bold line leftwards (not correct as -12 is not related).
- **B**: Open circle at -3, bold line leftwards (not correct as -3 is not related).
- **C**: Open circle at -3, bold line rightwards (not correct).
- **D**: Open circle at -12, bold line rightwards (not correct).

None of the provided options show a correct representation of the inequality \( x < 3 \).

Since there are no provided graphs for \( x < 3 \), you might need to reconsider or check the specific graphs again. If there is no option for open circle at 3 with bold line leftwards, the options as provided do not illustrate the solution correctly.