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Solving One-Step Equations & InequalitiesPowerPoint Presentation

Solving One-Step Equations & Inequalities

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### CONGRATULATIONS!!!

Try to solve without using a calculator!!!

4

Solving Equations: x and ÷

Click on the topics in order to learn moreabout them:

5

Multiplication Property

6

1

Division Property

Solving Equations: + and -

7

Inequalities

2

Addition Property

8

Solving an Inequality

3

Subtraction Property

Review

Solve Equations using Addition and Subtraction

- 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.

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Addition Property of Equality

- 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

Solve by Adding

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

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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

Solve by Subtracting

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

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Solve Equations using Multiplication and Division

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.

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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

Solve by Multiplying

(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

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Division Property of Equality

- 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

Solve by Dividing

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

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

Divide both sides by -5 to get x by itself

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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.

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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

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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

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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!

TRY AGAIN!

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

Back to question

CORRECT!!

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

Click to continue

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!

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

Click to continue

Click the pencils to return to the title slide for the next student:

You have completed this lesson on Solving Equations and Inequalities

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