Question

which number line shows the solution to (\frac{1}{4}x + 1 < 5)?

Explanation:

Step1: Solve the inequality for \( x \)

Start with the inequality \( \frac{1}{4}x + 1 < 5 \). Subtract 1 from both sides:
\( \frac{1}{4}x + 1 - 1 < 5 - 1 \)
Simplify: \( \frac{1}{4}x < 4 \).

Step2: Multiply both sides by 4

Multiply each side by 4 to isolate \( x \):
\( 4 \times \frac{1}{4}x < 4 \times 4 \)
Simplify: \( x < 16 \).

Answer:

The number line with an open circle at 16 and a red arrow pointing to the left (toward numbers less than 16, like 13, 14, 15) is the solution. This corresponds to the last number line (with 13–19) showing \( x < 16 \).