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## Pre-algebra

### 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

Symbol | Meaning |
---|---|

is greater than | Greater than |

start underline, is greater than, end underline | Greater than or equal to |

is less than | Less than |

start underline, is less than, end underline | 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, 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.

Now, we simplify.

**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.

Now, we simplify.

*Want to learn more about one-step inequalities? Check out this video.*

### Practice set 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.

Now, we simplify.

**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.

Now, we simplify.

### Practice set 2

*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(19 votes)
- 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.(34 votes)

- How can anyone do this.(22 votes)
- Just read the article more carefully and you will understand.(4 votes)

- I keep getting confused on when to switch or not(15 votes)
- me to.

I keep forgetting.(4 votes)

- Math needs to solve its own problems. I'm not a life expert!(15 votes)
- 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.(2 votes)

- this is not the way my teacher teached me(11 votes)
- 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.(8 votes)

- 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(9 votes)
- 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.(5 votes)

- i kind of get it but still to hard for me.(5 votes)
- 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

and that is your answer.

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.

the answer will be h<-0.25(7 votes)

- on the last question why did the symbol switch(4 votes)
- The symbol switched because when you divide/multiply a negative number in an INEQUALITY the symbol must change.(6 votes)

- For the last question in the second exercise, problem 2c, can we not equally put x is less than or equal to 3 1/3?(7 votes)
- i like pizza(5 votes)