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Video: Finding Solutions for Double Linear Inequalities in Interval Notation

Bethani Gasparine

Find all values of 𝑥 that satisfy 4 + 𝑥 < 2𝑥 − 5 < 7 + 𝑥. Write your answer as an interval.

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Video Transcript

Find all values of 𝑥 that satisfy four plus 𝑥 is less than two 𝑥 minus five that’s less than seven plus 𝑥. Write your answer as an interval.

With our inequality, we need to find all values of 𝑥 as an interval, that will satisfy this inequality. So we need to get that middle 𝑥 all alone. So the first thing we need to do is add five to both sides as well as in the middle, so it cancels. Now that we’ve gotten rid of the minus five, we have two 𝑥 in the middle. So we have two 𝑥s. We only nee- want one, so let’s subtract 𝑥. And we’re left with nine is less than 𝑥 is less than twelve.

So the interval that satisfies this inequality is from nine until twelve. So the numbers need to be greater than nine but less than twelve.