Question

What are the steps to solve this inequality? And which number line is correct? (The green area is the shaded region.)

−8+4x<−4
−
8
+
4
𝑥
<
−
4


(1 point)
Responses

Subtract 8 and divide by 4, x<1
𝑥
<
1

Subtract 8 and divide by 4, x<1
𝑥
<
1

Add 8 and divide by 4, x<1
𝑥
<
1

Add 8 and divide by 4, x<1
𝑥
<
1

Add 8 and divide by 4, x<1
𝑥
<
1

Add 8 and divide by 4, x<1
𝑥
<
1

Add 8 and multiply by 4, x<1
𝑥
<
1

Add 8 and multiply by 4, x<1
𝑥
<
1

Answer 1

To solve the inequality \(-8 + 4x < -4\), follow these steps:

1. **Add 8 to both sides**:
\[
-8 + 4x + 8 < -4 + 8
\]
This simplifies to:
\[
4x < 4
\]

2. **Divide both sides by 4**:
\[
\frac{4x}{4} < \frac{4}{4}
\]
This simplifies to:
\[
x < 1
\]

Thus, the solution to the inequality is:
\[
x < 1
\]

Regarding the number line, the correct representation would shade all numbers to the left of 1, indicating that \(x\) can be any number less than 1. The endpoint at 1 would typically be open (not filled) since 1 itself is not included in the solution (as indicated by the "<" sign).

From the responses provided:
- The correct step is to **Add 8 and divide by 4, x < 1**.
- Therefore, "Add 8 and divide by 4, x < 1" is the correct choice.

If the green area represents the shaded region on the number line, it should be to the left of 1 without including 1 itself.