Question

section a
show the inequalities on the number line
x + 2
-2.5 < x ≤ 12.5
section b
solve the following inequalities and show the solution on the number line
x + 3 ≥ 8
x + 5 ≤ -4
3x < 30
x + 8 > 27

1. \\(\frac{x}{6} < 12\\)
2. \\(\frac{x}{8} + 1 ≤ 7\\)
3. \\(\frac{x}{3} - 3 ≥ 9\\)
4. \\(\frac{4x + 4}{4} < 7\\)
5. \\(\frac{2x - 8}{4} > -4\\)

Explanation:

Step1: Solve \( \frac{x}{6} < 12 \)

Multiply both sides by 6 to isolate \( x \).
\( \frac{x}{6} \times 6 < 12 \times 6 \)
\( x < 72 \)

Step2: Represent on number line

Draw an open circle at 72 (since \( x < 72 \), not \( x \leq 72 \)) and shade the line to the left of 72.

Answer:

The solution to \( \frac{x}{6} < 12 \) is \( x < 72 \), represented on the number line with an open circle at 72 and shading leftward.