If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# One-step inequalities review

Review evaluating one-step inequalities, and try some practice problems.

## Inequalities symbols

SymbolMeaning
is greater thanGreater than
start underline, is greater than, end underlineGreater than or equal to
is less thanLess than
start underline, is less than, end underlineLess than or equal to

## Evaluating inequalities with addition and subtraction

We evaluate inequalities like we evaluate equations: we want to isolate the variable.
Example 1: x, plus, 7, is greater than, 4
To isolate x, let's start color #11accd, start text, s, u, b, t, r, a, c, t, space, end text, 7, end color #11accd from both sides.
x, plus, 7, start color #11accd, minus, 7, end color #11accd, is greater than, 4, start color #11accd, minus, 7, end color #11accd
Now, we simplify.
x, is greater than, minus, 3
Example 2: z, minus, 11, space, start underline, is less than, end underline, 5
To isolate z, let's start color #1fab54, start text, a, d, d, space, end text, 11, end color #1fab54 to both sides.
z, minus, 11, start color #1fab54, plus, 11, end color #1fab54, space, start underline, is less than, end underline, 5, start color #1fab54, plus, 11, end color #1fab54
Now, we simplify.
z, space, start underline, is less than, end underline, 16

### Practice set 1

Problem 1A
Solve for x.
x, minus, 8, is less than, minus, 1

## Evaluating inequalities with multiplication and division

Again, we want to isolate the variable. But things will get a little different when multiply or divide by a negative number. Look carefully to see what happens!
Example 1: 10, x, is less than, minus, 3
To isolate x, let's divide both sides by 10.
start fraction, 10, x, divided by, 10, end fraction, is less than, start fraction, minus, 3, divided by, 10, end fraction
Now, we simplify.
x, is less than, minus, start fraction, 3, divided by, 10, end fraction
Example 2: start fraction, y, divided by, minus, 6, end fraction, space, start underline, is greater than, end underline, space, 4
To isolate y, let's multiply both sides by minus, 6.
left parenthesis, start fraction, y, divided by, minus, 6, end fraction, right parenthesis, times, minus, 6, space, start underline, is greater than, end underline, space, 4, times, minus, 6
Now, we simplify.
y, space, start underline, is less than, end underline, minus, 24

### Practice set 2

Problem 2A
Solve for x.
2, x, is less than, 15

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• How am I suppose to know when to flip the inequality if you re suppose to
• You are supposed to flip an inequality when you multiply or divide either side by a negative number. You do this because when multiplying sides by a negative number, you change the sign of each side, making the previously greater side less.
• How can anyone do this.
• Just read the article more carefully and you will understand.
• this is not the way my teacher teached me
• Can someone help me i get confused when it comes to switch the sign do you flip it when it has a negative in the problem or do you flip the sign when is a negative.
• I keep getting confused on when to switch or not
• me to.
I keep forgetting.
• I'm having trouble with entering data & answers in "One-step inequalities" Review. First, I can not enter my answers because the POP-UP icons won't clear. Specifically, the problem "2x<15". At the present, the entire Exercise "One-Step Inequalities Review" is LOCKED-UP. Please Help. Henry
• Just click the screen to the left, right, top, or bottom of the pop-up. It should clear just fine. If it doesn't, sorry, maybe your device has a glitch.
• on the last question why did the symbol switch