Main content

## Pre-algebra

### Unit 7: Lesson 7

Intro to inequalities with variables- Testing solutions to inequalities
- Testing solutions to inequalities (basic)
- Plotting inequalities
- Plotting an inequality example
- Graphing basic inequalities
- Inequality from graph
- Plotting inequalities
- Inequalities word problems
- Inequalities word problems
- Graphing inequalities review

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# Graphing inequalities review

CCSS.Math:

Review graphing inequalities with variables on number lines, and then try some practice problems.

## Inequalities

**Inequalities**show the relation between two expressions that are not equal.

Below are some examples of inequalities:

### 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 |

## Graphing inequalities with variables

We can use a number line to show the possible solutions to an inequality.

**Example 1: x, is greater than, 4**

An inequality like x, is greater than, 4 tells us that x can be any value

**greater than 4.**We can show this on a number line by putting an open circle on 4 and shading the numbers that are greater than 4.

**Example 2: y, space, start underline, is less than, end underline, space, 3**

If we have either the start underline, is greater than, end underline or start underline, is less than, end underline symbol in our inequality, we shade in the circle to show that the variable may be equal to that number.

For example, y, space, start underline, is less than, end underline, space, 3 is graphed as follows:

This number line shows that

**y is either equal to 3 or less than 3.***Want to learn more about graphing inequalities? Check out this video.*

## Practice

*Want to try more problems like this? Check out these exercises:*

Inequality from graph

Plotting inequalities

## Want to join the conversation?

- ok so umm we have to find the inequalities by know what's less than and greater than right?(21 votes)
- Yes, does this mean you get the two confused? If you make the sign with your left hand (<), left is less. If you make the sign with your right hand (>), Tony the Tiger says right is Grrrrrrrrreater.(28 votes)

- The questions were easy, but didn't really make me think. And if i do get those my teacher should only assign like 3(18 votes)
- Most of the questions were easy however my teacher loves to assign few but very tricky questions.(5 votes)

- i dont understand why circles need to be full or hollow(6 votes)
- Full circle means we
**include**the number:

X ≥ 3 This means X can be 3**OR**greater

Hollow circle means we do**NOT**include the number:

X > 3 This means X can**ONLY**be greater than 3(25 votes)

- Whats a good way to memorize which way the line on the number line goes? I keep forgetting.(5 votes)
- If the variable is on the left, the inequality tells you which way to draw the line. For example:

x<6

Notice the inequality is pointing to the left, so your line goes to the left.

x>6

Notice the inequality points to the right, the line goes to the right.

Alternatively, you need to know that the smaller numbers are on the left of the number line and the larger numbers are to the right. A common tip used to help students remember what each inequality symbol means it to think of the symbol as the mouth of a hungry alligator. Its open mouth will always face the larger value.

6>x

Notice, the alligator wants to eat the 6 so it is larger than x. So, x must be numbers smaller than 6 and your line would get drawn to the left.

6<x

Notice, the alligator wants to eat the X, so the x is larger than 6 and your line needs to be to the right of the 6.

Hope this helps.(8 votes)

- This is very wise, and relatable.(10 votes)

- I dont understand some of the questions(5 votes)
- some of them are to trick you reread them(5 votes)

- How do you know if a word problem wants us to have the circle opened or closed? Are there key words, or certain things we have to look for?(6 votes)
- if the problem is a <> with the line under which means equal too, as well. You close the circle since you include the number.(2 votes)

- I don´t understand some of the questions(5 votes)
- Some are meant to trick you just reread the problem.(2 votes)

- Why does the open and close circle needed??(3 votes)
- These show if the point counts (closed circle and use of ≥ or ≤) or does not count (open circle and use of < or >). On a coordinate plane, it turns into an solid line or a dashed line.(4 votes)

- What is a dependent variable?(3 votes)