What is a Linear Inequality?
- A linear inequality is an equation that involves linear functions. An equation also includes one symbol of inequality:
- < is less than
- > is greater than
- ≤ is less than or equal to
- ≥ is greater than or equal to
- ≠ is not equal to
- = is equal to
- A linear inequality ressembles just like the linear equations from the last unit, except with an inequality symbol to replace the equal sign.
What do these Equations Mean?
- If we were to write “x<4”, that would be that a number is less than four. Same goes for “x>4”, which would mean that a number is greater than four.
- If we write “x≤4” that would mean that a number is less or equal to four. Same goes for “x≥4”, which would mean that a number is greater or equal to four.
How do you Graph a Linear Inequality?
- When graphing linear inequalities on number lines, we use different types of dots to identify the inequality sign. if it’s an open dot, we use those for equations that contain less or greater signs. If it’s a closed dot, we use those for equations that contain less or equal to, and greater or equal to signs.
Here are some examples of linear inequalities plotted onto graphs:
(Graph 1: x<-2, Graph 2: x≤-2, Graph 3: x>-2, Graph 4: x≥-2)
How do you Solve Linear Inequalities?
- Solving linear inequality equations is just like solving normal linear equations,
- One thing that always helps me is to remember is
These will help you remember what to do first when you are solving your equation.
- Here is an example of the steps of solving the linear inequality equation “2x+4>3x+1”..
- If an answer to an inequality equation is negative, you have to switch the sign to the opposite sign.