Question

Solve $\frac{1}{3} t - 5 < t - 2 \le -3t + 7.$ Give your answer as an interval.

Answer 1

t ∈ (-4.5, 2.25]

Explanation:

You want to solve the compound inequality ...

1/3t -5 < t -2 ≤ -3t +7

Split

We can divide this into two inequalities.

1/3t -5 < t -2 ⇒ -3 < 2/3t ⇒ -4.5 < t

and

t -2 ≤ -3t +7 ⇒ 4t ≤ 9 ⇒ t ≤ 2.25

Solution interval

The solution interval is the intersection of these two solutions:

-4.5 < t ≤ 2.25

t ∈ (-4.5, 2.25]

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