1 / 25

# Solving One-Step Equations & Inequalities - PowerPoint PPT Presentation

Solving One-Step Equations & Inequalities. 6 th Grade Mathematics Miss Muhr. Click to continue. Try to solve without using a calculator!!!. 4. Solving Equations: x and ÷. Click on the topics in order to learn more about them:. 5. Multiplication Property. 6. 1. Division Property.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Solving One-Step Equations & Inequalities' - angelo

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Solving One-Step Equations & Inequalities

Miss Muhr

Click to continue

4

Solving Equations: x and ÷

5

Multiplication Property

6

1

Division Property

Solving Equations: + and -

7

Inequalities

2

8

Solving an Inequality

3

Subtraction Property

Review

• In an equation, the variable represents the number that satisfies the equation. To solve an equation means to find the value of the variable that makes the equation true.

• The process of solving an equation starts with getting the variable on one side of the equation by itself. Each step results in an equivalent equation. Equivalent equations have equal solutions.

• If an equation is true and the same number is added to each side of the equation, the produced equivalent equation is also true.

• For any real numbers a, b, and c, if a = b, then a + c = b + c.

14 = 1414 + 3 = 14 + 317 = 17

-3 = -3+9 +96 = 6

Click to continue

Horizontal Method

Vertical Method

x – 45 = 78+ 45 +45x = 123

x – 45 = 78x – 45 + 45 = 78 + 45x = 123

Check: x – 45 = 78123 – 45 = ? = 7878 = 78 ✓

Add 45 to both sides to get x by itself

Subtraction Property of Equality

• If an equation is true and the same number is subtracted from each side of the equation, the produced equivalent equation is also true.

• For any real numbers a, b, and c, if a = b, then a - c = b - c.

87 = 8787 -17 = 87 -1770 = 70

13 = 13-28 -28-15 = -15

Click to continue

Horizontal Method

Vertical Method

24 + x = 61- 24 - 24x = 37

24 + x = 6124 – 24 + x = 61 – 24x = 37

Check:24 + x = 6124 + 37 = ? = 6161 = 61 ✓

Subtract 24 from both sides to get x by itself

In an equation x/2 = 6, the variable x is divided by 2. To solve for x, undo the division by multiplying each side by 2.

This is an example of the Multiplication Property of Equality.

Multiplication Property of Equality

• If an equation is true and each side is multiplied by the same nonzero number, the produced equivalent equation is also true.

• For any real numbers a, b, and c, if a = b, then ac = bc.

• Example: If x = 5, then 3x = 15.

Click to continue

(3/5)x = 1/3(5/3) (3/5)x = (1/3) (5/3)x = 5/9

Check:(3/5)x = 1/3(3/5) (5/9) = ? = 1/31/3 = 1/3 ✓

Multiply both sides by the reciprocal to get x by itself

• If an equation is true and each side is divided by the same nonzero number, the produced equivalent equation is also true.

• For any real numbers a, b, and c, c ≠ 0, if a = b, then a/c = b/c.

• Example: If x = -20, then x/5 = -20/5 or -4.

Click to continue

70 = -5x-5 -5-14 = x

Check:70 = -5x70 = ? = -5(-14)70 = 70 ✓

Divide both sides by -5 to get x by itself

>

Inequalities

• An inequality, similar to an equation, has two expressions split by a symbol that indicates how one expression is related to the other.

• In an equation such as 8x = 64, the = sign indicates that the expressions are equivalent. In an inequality, such as 8x > 64, the > sign indicates that the left side is larger than the right side.

>

Solving an Inequality ( > “greater than” )

To solve the inequality 8x > 64, follow the same rules that you did for equations. In this example, divide both sides by 8so that x > 8.

8x > 648 8x > 8

This means that x is a value and it is always larger than 8, and never equal to or less than 8.

Click to continue

>

Solving an Inequality(< “less than”)

4x < 884 4x < 22

So… xis a value and it is always smaller than 22, and never equal to or greater than 22.

Divide both sides by 4 to get x by itself

Review:Solving Equations

Solve for x.

3 + x = 27

(a.) x = 30

(b.) x = 24

(c.) x = 25

Use pencil and paper if you need to!

You are close! Go back and think about what the Subtraction Property of Equality is…

Back to question

Great work! You remembered to subtract the same number from both sides to produce equivalent equations.

Click to continue

Go back and make sure you double check your work…

Back to question

Review – Solving Inequalities

Solve for x.

9x < 63

(a.) x < 7

(b.) x < 567

(c.) x > 7

Use pencil and paper if you need to!

>

CORRECT!!

Awesome! You remembered to isolate the variable on one side in order to solve the inequality.

Click to continue

>

Try Again!

Remember… use the Division Property to get the variable by itself.

Back to question

>

Try Again!