# How do I use a sign chart to solve #2< -16t^2+6<5#?

##### 1 Answer

#### Explanation:

Here, we have two inequalities that must be satisfied.

**(1)**

**(2)**

**(1) The first inequality**

We write the inequality in **standard form** by putting all non-zero terms on the left side.

We start by finding the **critical numbers**.

Set

The critical numbers are

We have three intervals to consider: (-∞, -0.5), (-0.5, 0.5), and (0.5, ∞).

We pick a test number and evaluate the function and its sign at that number.

**(2) The second inequality**

The inequality in standard form is

Set

The critical numbers are

The three intervals to consider are: (-∞, -0.25), (-0.25, 0.25), and (0.25, ∞).

Now we create a sign chart for the two functions.

The only intervals for which the two signs are both negative are (-0.5, -0.25) and (0.25, 0.5).