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

Question

−8+4x<−4

(1 point)
Responses

Subtract 8 and divide by 4, x<1

Subtract 8 and divide by 4, x<1

Add 8 and divide by 4, x<1

Add 8 and divide by 4, x<1

Add 8 and divide by 4, x<1

Add 8 and divide by 4, x<1

Add 8 and multiply by 4, x<1

Add 8 and multiply by 4, x<1

Answer 1

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

1. Add 8 to both sides to isolate the term with \( x \): \[ -8 + 4x + 8 < -4 + 8 \] \[ 4x < 4 \]

2. Divide both sides by 4 to solve for \( x \): \[ \frac{4x}{4} < \frac{4}{4} \] \[ x < 1 \]

So, the correct response is: Add 8 and divide by 4, \( x < 1 \).

As for the number line, since \( x < 1 \) indicates that \( x \) can take any value less than 1, the correct number line should show a shaded region extending left from 1 (but not including 1). The point at 1 itself should typically be marked with an open circle to indicate that it is not included in the solution.

If the green area represents the shaded region that satisfies the inequality, it should depict values less than 1.