# How do you solve and graph #-4<2t-6<8#?

See a solution process below:

First, add

Now, divide each segment by

Or

Or, in interval notation:

To graph this we will draw vertical lines at

The lines will be dashed lines because both inequality operators do not contain an "or equal to" clause.

We will shade between the lines to show the interval:

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To solve the compound inequality -4 < 2t - 6 < 8, you first isolate the variable by adding 6 to all parts of the inequality:

-4 + 6 < 2t - 6 + 6 < 8 + 6 2 < 2t < 14

Next, divide all parts of the inequality by 2:

2/2 < 2t/2 < 14/2 1 < t < 7

The solution to the compound inequality is 1 < t < 7.

To graph this solution on a number line, you would plot an open circle at 1 and at 7, indicating that they are not included in the solution. Then, shade the region between the two points to represent all the values of t that satisfy the inequality.

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