Question

solve the linear inequality. other than ∅, use interval notation to express the the solution set on a number line.
2x + 4 < 20
options:
(8, ∞)
(-∞, 8
(-∞, 8)
8, ∞)

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( x \), we subtract 4 from both sides of the inequality \( 2x + 4 < 20 \). This gives us \( 2x + 4 - 4 < 20 - 4 \), which simplifies to \( 2x < 16 \).

Step2: Divide both sides by 2

Next, we divide both sides of the inequality \( 2x < 16 \) by 2 to solve for \( x \). This gives us \( \frac{2x}{2} < \frac{16}{2} \), which simplifies to \( x < 8 \).
In interval notation, the solution to \( x < 8 \) is \( (-\infty, 8) \), and the number line representation should have an open circle at 8 (since 8 is not included in the solution set) and an arrow pointing to the left (indicating all numbers less than 8).

Answer:

\( (-\infty, 8) \) (corresponding to the option with the open circle at 8 and arrow to the left on the number line)