Question

question
solve for x and graph the solution on the number line below.
15 ≥ 3x − 3 > −12
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
click and drag to plot line
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Explanation:

Step1: Add 3 to all parts

To solve the compound inequality \(15 \geq 3x - 3 > -12\), we first add 3 to each part of the inequality. This is done to isolate the term with \(x\).
\[
15 + 3 \geq 3x - 3 + 3 > -12 + 3
\]
Simplifying each part:
\[
18 \geq 3x > -9
\]

Step2: Divide all parts by 3

Next, we divide each part of the inequality by 3 to solve for \(x\).
\[
\frac{18}{3} \geq \frac{3x}{3} > \frac{-9}{3}
\]
Simplifying each part:
\[
6 \geq x > -3
\]
Which can also be written as \(-3 < x \leq 6\)

Answer:

Inequality Notation: \(-3 < x \leq 6\)

For the number line: We would plot an open circle at \(-3\) (since \(x > -3\), not including \(-3\)) and a closed circle at \(6\) (since \(x \leq 6\), including \(6\)), and then draw a line segment connecting these two points.