High School Math Solutions – Inequalities Calculator, Linear Inequalities

Solving linear inequalities is pretty simple. A linear inequality is an inequality which involves a linear function. Think of a linear inequality as a linear equation. You solve a linear inequality just like you would a linear equation, by isolating the variable using algebraic manipulations.

One thing to note: if you divide or multiply a linear inequality by a negative number you must switch the inequality sign. That means if you have -2y\le4 and you divide the linear inequality by -2 to isolate y, then the sign switches to ≥. The inequality becomes y\ge2.

Let’s see some examples.

First example (click here):

By using simple algebra, x was isolated and the answer was calculated. You can see that the sign was switched because the inequality was multiplied by -2.


Second example (click here):

Last example (click here):

Solving linear inequalities is pretty simple if you’ve solved linear equations before. As long as you remember to switch the inequality sign when multiplying or dividing the inequality by a negative number, then you are good to go! If you need more help or practice on this topic, check out Symbolab’s inequality practice.

Until next time,

Leah