How do you check to see if a number is in the solution set of an inequality?

Nov 2, 2014

You can check by plugging the value into the left-hand side and the right-hand side of the inequality separately to see resulting values satisfy the inequality.

Example

Is $x = 3$ a solution of the inequality $2 x - 3 < x + 1$?

$\left(L H S\right) = 2 \left(3\right) - 3 = 6 - 3 = 3$

$\left(R H S\right) = \left(3\right) + 1 = 4$

Since $\left(L H S\right) < \left(R H S\right)$, $x = 3$ is a solution of the inequality.

I hope that this was helpful.