Question

solve for x and graph the solution on the number line below. 33 ≥ 4x - 3 ≥ 9 answer attempt 1 out of 2 < > ≤ ≥ or inequality notation: number line: -12 -8 -4 0 4 8 10 12

Explanation:

Step1: Add 3 to all parts

To solve the compound inequality \( 33 \geq 4x - 3 \geq 9 \), we first add 3 to each part of the inequality. This is done to isolate the term with \( x \).
\[
33 + 3 \geq 4x - 3 + 3 \geq 9 + 3
\]
Simplifying each part:
\[
36 \geq 4x \geq 12
\]

Step2: Divide all parts by 4

Next, we divide each part of the inequality by 4 to solve for \( x \).
\[
\frac{36}{4} \geq \frac{4x}{4} \geq \frac{12}{4}
\]
Simplifying each fraction:
\[
9 \geq x \geq 3
\]
We can also write this as \( 3 \leq x \leq 9 \).

Answer:

Inequality Notation: \( 3 \leq x \leq 9 \)

For the number line: We would mark a closed circle at 3 and a closed circle at 9 (since the inequality is "less than or equal to" and "greater than or equal to"), and shade the region between 3 and 9 on the number line.