Question

solve for y.
5 ≥ 3y - 1 ≥ -1
write your answer as a compound inequality with integers.

Explanation:

Step1: Add 1 to all parts

To solve the compound inequality \(5 \geq 3y - 1 \geq -1\), we first add 1 to each part of the inequality. This is done to isolate the term with \(y\).
\[
5 + 1 \geq 3y - 1 + 1 \geq -1 + 1
\]
Simplifying each part, we get:
\[
6 \geq 3y \geq 0
\]

Step2: Divide all parts by 3

Next, we divide each part of the inequality by 3 to solve for \(y\).
\[
\frac{6}{3} \geq \frac{3y}{3} \geq \frac{0}{3}
\]
Simplifying each part, we obtain:
\[
2 \geq y \geq 0
\]
We can also write this as \(0 \leq y \leq 2\) (since the inequality \(a \geq b \geq c\) is equivalent to \(c \leq b \leq a\)).

Answer:

\(0 \leq y \leq 2\)