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### Course: 7th grade (Illustrative Mathematics) > Unit 6

Lesson 8: Lesson 15: Efficiently solving inequalities# One-step inequalities review

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

## Inequalities symbols

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

Greater than | |

Greater than or equal to | |

Less than | |

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 ${\text{subtract}7}$ from both sides.

Now, we simplify.

**Example 2:**$z-11{\textstyle \phantom{\rule{0.167em}{0ex}}}\text{}\underset{\u2015}{}{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}5$

To isolate $z$ , let's ${\text{add}11}$ 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 we 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 $10$ .

Now, we simplify.

**Example 2:**$\frac{y}{-6}}{\textstyle \phantom{\rule{0.167em}{0ex}}}\text{}\underset{\u2015}{}{\textstyle \phantom{\rule{0.167em}{0ex}}}\text{}4$

To isolate $y$ , let's multiply both sides by $-6$ .

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(23 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.(59 votes)

- Math needs to solve its own problems. I'm not a life expert!(36 votes)
- math is important! i think we should definitely learn these different kinds of math (variables, negatives, etc) but we shouldn’t spend MONTHS on ONE subject!(1 vote)

- How can anyone do this.(25 votes)
- it is confusing but it takes practice(0 votes)

- I keep getting confused on when to switch or not(16 votes)
- me to.

I keep forgetting.(3 votes)

- This math aint' mathin' and my brain aint' brainin'(14 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(11 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.(6 votes)

- i kind of get it but still to hard for me.(7 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(11 votes)

- this is not the way my teacher teached me(9 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.(7 votes)

- we have to change the symbols when he have a negative number?(4 votes)
- We reverse the inequality only if we multiply or divide both sides of the inequality by a negative number.

Hope this helps.(9 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?(8 votes)