Video: Finding the Solution Set of a Linear Inequality as an Interval

Find the solution set of the inequality −2𝑥 + 3 ⩽ 5. Write your answer as an interval.

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Video Transcript

Find the solution set of the inequality negative two 𝑥 plus three is less than or equal to five. Write your answer as an interval.

The first part of this question will involve solving the inequality using two steps. We will, then, write this answer as an interval. The inequality negative two 𝑥 plus three is less than or equal to five can be solved using inverse operations. Our first step is to subtract three from both sides of the inequality. As five minus three is equal to two, we have negative two 𝑥 is less than or equal to two. Our second and final step is to divide both sides of the inequality by negative two. We do need to be careful here as we recall, if negative 𝑥 is less than four, then 𝑥 is greater than negative four.

When dividing an inequality by a negative number, the sign also changes. Negative two 𝑥 divided by negative two is 𝑥. Two divided by negative two is negative one. If negative two 𝑥 is less than or equal to two, then 𝑥 is greater than or equal to negative one. This means that 𝑥 can take any value greater than or equal to negative one. We were asked to write this as an interval, so 𝑥 is greater than or equal to negative one but less than ∞. The equal to part of the inequality means that we have a square bracket next to negative one. ∞ and negative ∞ will always have a curly bracket or parentheses as we can never reach these values.

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