Question

Which values of
x
make the inequality below true?

5
−
3
x
+
3
≤
13

A.
x
≥
−
7

B.
x
≥
−
5
3

C.
x
≥
−
11
3

D.
x
≥
−
5

Answer 1

To solve the inequality \( 5 - 3x + 3 \leq 13 \), we will first simplify the left side of the inequality:

1. Combine the constant terms:
\[
5 + 3 = 8
\]
So the inequality becomes:
\[
8 - 3x \leq 13
\]

2. Next, we'll isolate the term involving \( x \):
\[
-3x \leq 13 - 8
\]
\[
-3x \leq 5
\]

3. Now, divide both sides by \(-3\). Remember that when you divide or multiply by a negative number, you need to flip the inequality sign:
\[
x \geq \frac{5}{-3}
\]
Simplifying \( \frac{5}{-3} \) gives:
\[
x \geq -\frac{5}{3}
\]

Thus, the correct answer is:

**B. \( x \geq -\frac{5}{3} \)**