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### Course: Pre-algebra>Unit 10

Lesson 7: One-step inequalities

# One-step inequalities review

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

## Inequalities symbols

SymbolMeaning
$>$Greater than
$\underset{―}{>}$Greater than or equal to
$<$Less than
$\underset{―}{<}$Less 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: $x+7>4$
To isolate $x$, let's from both sides.
$x+7-7>4-7$
Now, we simplify.
$x>-3$
Example 2:
To isolate $z$, let's to both sides.
Now, we simplify.

### Practice set 1

Problem 1A
Solve for $x$.
$x-8<-1$

## 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: $10x<-3$
To isolate $x$, let's divide both sides by $10$.
$\frac{10x}{10}<\frac{-3}{10}$
Now, we simplify.
$x<-\frac{3}{10}$
Example 2:
To isolate $y$, let's multiply both sides by $-6$.
Now, we simplify.

### Practice set 2

Problem 2A
Solve for $x$.
$2x<15$

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.
• Math needs to solve its own problems. I'm not a life expert!
• AGREED LOL. but sadly we have to and it can become really fun, if you have toys pretend that you are having a class and they are the students. You dont even have to talk, just the idea of it helps me.
• How can anyone do this.
• What do you mean, I did it lol
• 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.
• i kind of get it but still to hard for me.
• if you want to add or subtract you have to put the x alone example: h+3<8
you will subtract the 2 sides by 3
h+3<8
-3 -3
h<5

same goes for multiplting and dividing but it has only one diffrent rule in -/+ you never change the sign but in x/dividing when ever you multiply or divid with a negative number you must change the sign
example: -5h>20 when you see a number stuck to a varibale than you must now that there is a hiden multipication sign so what is the opposit of the multipication. division so, -5 divided by 20 is -0.25
and dont forget when ever you multiply of divide by a negative number you change the inequality sign.
• 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.