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Solving One-Step Equations & Inequalities

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Solving One-Step Equations & Inequalities

6th Grade Mathematics

Miss Muhr

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Try to solve without using a calculator!!!

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Solving Equations: x and ÷

Click on the topics in order to learn moreabout them:

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Multiplication Property

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1

Division Property

Solving Equations: + and -

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Inequalities

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Addition Property

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Solving an Inequality

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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.

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- 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

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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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- 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

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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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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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- 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.

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(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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- 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.

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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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- 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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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.

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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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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…

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

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Go back and make sure you double check your work…

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

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

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Go back and check the direction of your sign in the inequality.

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

CONGRATULATIONS!!!

You have completed this lesson on Solving Equations and Inequalities