4

Inequalities

Inequalities are similar to equations. There is only one difference from the way the an inequality looks and a equation looks. Instead of an equal sign there is an angled bracket, which means that the one side is either greater than or less than the other. Sometimes there is a line underneath, which means that the equations could aslo be equal to each other.

Sign Meaning
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to

Examples

  1. 3x + 4 > 5

    2. We can rewrite the inequality as an equation and deal with the sign later.

    Step 1. Rewrite the inequality.
    3x + 4 = 7
    Step 2. Subtract 4 from both sides.
    3x + 4 - 4 = 7 - 4
    3x = 3

    Now it's just a simple one-step equation. We can also rewrite the equation removing the equal sign and replacing it with the original greater than sign.

    3x / 3
    >
    3 / 3

    Step 3. Rewriting the inequality once more we get our final answer.
    x > 1.
    Step 4. We can plug any number in for x that is greater than 1 and that number will satisfy the equation. Let's pick a number greater than 1, let's try 2.
    3(2) + 4 > 7
    6 + 4 > 7
    10 > 7 ✓
    As we can see 10 is greater than 7 so our answer for our inequality is correct. Back to top