Question

How do you solve `14\leq 2t + 18< 20`?

Answer 1

Subtract `18` on each side to get:

`-4 ≤ 2t < 2`

Simplify to get:

`-2 ≤ t < 1`

Explanation:

To start, treat the inequality signs as equal signs. This will be changed later on. Remember that what you do to one side of the inequality, you must do to the other.

To solve for `t`, we must isolate it. The only way to do that would be to subtract `18`. So it becomes:

`14 (-18) ≤ 2t + 18 (-18) < 20 (-18)`

simplifies to

`-4 ≤ 2t < 2`

Now, we must further isolate `t`. To do so, we divide each side by `2`:

`-4/2 ≤ (2t)/2 < 2/2`

simplifies to

`-2 ≤ t < 1`

which is your answer