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Solving Linear Inequalities - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

If we want to solve for or describe a region in a coordinate plane, we can use linear inequalities. Linear inequalities give us a set of solutions as opposed to just one solution. Solving linear inequalities uses similar methods as solving multi-step equations, except that there are extra rules when using multiplication and division. We graph linear inequalities by shading regions of number lines or coordinate planes.

Solving linear inequalities, how we solve linear inequalities is very similar to how we solve linear equalities. Same properties, the only thing we have to be careful of is that if we ever divide by a negative we need to make sure we flip our inequality sign. So for this problem right here, first thing we want to do is isolate our variable which is our x so we add the 5 to the other side. End up with 2x is less than 8 to solve for x divide by 2, x is less than 4, got our x by itself. In this case our answer is actually a region any number less than 4, so we actually have a number of answers that will satisfy this equation.

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