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.
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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!!!
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
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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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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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(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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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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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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CONGRATULATIONS!!!
You have completed this lesson on Solving Equations and Inequalities