Which values of

Question

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 can first simplify it:

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

2. Next, subtract 8 from both sides: \[ -3x \leq 13 - 8 \] This simplifies to: \[ -3x \leq 5 \]

3. Now, divide both sides by \(-3\). Remember that dividing by a negative number reverses the inequality: \[ x \geq -\frac{5}{3} \]

This means the values of \(x\) that make the inequality true are those that are greater than or equal to \(-\frac{5}{3}\).

Thus, the correct answer is:

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