To solve the inequality \(-8 + 4x < -4\), follow these steps:
-
Add 8 to both sides: \[ -8 + 4x + 8 < -4 + 8 \] This simplifies to: \[ 4x < 4 \]
-
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.
1 answer