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.
