Name:____________________________________________
Solving Linear Equations: Classwork
Date:________
8 Grade Mathematics
th
Some things you have to remember in order to better understand solving equations.
Number Sets:

Natural Numbers: _____________________________________________________________________________________
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
Whole Numbers: ______________________________________________________________________________________
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
Integers: _____________________________________________________________________________________________
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Number Properties:

Commutative Property of Addition: _______________________________________________________________________
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
Commutative Property of Multiplication: ___________________________________________________________________
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
Associative Property of Addition: _________________________________________________________________________
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Associative Property of Multiplication: _____________________________________________________________________
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Identity of Addition: ____________________________________________________________________________________
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Identity of Multiplication: _______________________________________________________________________________
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Additive Inverse: : _____________________________________________________________________________________
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Multiplicative Inverse: __________________________________________________________________________________
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Multiplicative Property of Zero: __________________________________________________________________________
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Distributive Property: __________________________________________________________________________________
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Properties of Equality:

Addition Property: _____________________________________________________________________________________
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Subtraction Property: ___________________________________________________________________________________
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Multiplication Property: ________________________________________________________________________________
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Division Property: _____________________________________________________________________________________
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Steps for Solving Equations:
1.
Distribute
2.
Combine like terms
3.
Move variables to one side of the equation
4.
Move constants to the other side of the equation
5.
Solve
A Set of Guidelines for Solving Word Problems:
1.
Read the word problem once
2.
Write a statement that will answer the question being asked
3.
Try to determine how many steps it will take to find the answer to the questions
4.
Draw a picture to model the situation
5.
Write and equation based on your picture
6.
Solve the equation
7.
Ask yourself: “Does this make sense?”
Given the equation: 4 + 1 = 7 − 2, answer or complete the following:
1.
Is this equation true?
2.
Perform each of the following operations, and state whether or not the equation is still true:
3.
a.
Add three to both sides of the equal sign.
b.
Add three to the left side of the equal sign, and add two to the right side of the equal sign.
c.
Subtract six from both sides of the equal sign.
d.
Subtract three from one side of the equal sign, and subtract three from the other side of the equal sign.
e.
Multiply both sides of the equal sign by ten.
f.
Multiply the left side of the equation by ten and the right side of the equation by four.
g.
Divide both sides of the equation by two.
h.
Divide the left side of the equation by two and the right side of the equation by five.
What do you notice? Describe any patterns you see.
Solve the linear equation 2𝑥 − 3 = 4𝑥 for the number 𝑥.
3
Solve the linear equation 𝑥 − 21 = 15.
5
1
Solve the linear equations 𝑥 + 13 + 𝑥 = 1 − 9𝑥 + 22
5
Directions: For each problem, show your work, and check that your solution is correct.
1.
Solve the linear equation 𝑥 + 𝑥 + 2 + 𝑥 + 4 + 𝑥 + 6 = −28. State the property that justifies your first step and why you chose
it.
2.
Solve the linear equation 2(3𝑥 + 2) = 2𝑥 − 1 + 𝑥. State the property that justifies your first step and why you chose it.
3.
Solve the linear equation 𝑥 − 9 = 𝑥. State the property that justifies your first step and why you chose it.
4.
Solve the linear equation 29 − 3𝑥 = 5𝑥 + 5. State the property that justifies your first step and why you chose it.
5.
Solve the linear equation 𝑥 − 5 + 171 = 𝑥. State the property that justifies your first step and why you chose it.
3
5
1
3
Name:____________________________________________
Solving Linear Equations: Homework
Date:________
8 Grade Mathematics
th
Summary:
The properties of equality, shown below, are used to transform equations into simpler forms. If 𝐴, 𝐵, 𝐶 are rational numbers, then

If 𝐴 = 𝐵, then 𝐴 + 𝐶 = 𝐵 + 𝐶.
Addition property of equality

If 𝐴 = 𝐵, then 𝐴 − 𝐶 = 𝐵 − 𝐶.
Subtraction property of equality

If 𝐴 = 𝐵, then 𝐴 ⋅ 𝐶 = 𝐵 ⋅ 𝐶.
Multiplication property of equality

𝐴
𝐵
𝐶
𝐶
If 𝐴 = 𝐵, then = , where 𝐶 is not equal to zero
Division property of equality
To solve an equation, transform the equation until you get to the form of 𝑥 equal to a constant (𝑥 = 5, for example). To show that
you have read this summary circle your name at the top of this paper.
Directions: For each problem, solve each equation making sure to show all your work and check that your solution is correct.
1.
Solve the linear equation 𝑥 + 4 + 3𝑥 = 72. State the property that justifies your first step and why you chose it.
2.
Solve the linear equation 𝑥 + 3 + 𝑥 − 8 + 𝑥 = 55. State the property that justifies your first step and why you chose it.
3.
Solve the linear equation 𝑥 + 10 = 𝑥 + 54. State the property that justifies your first step and why you chose it.
4.
Solve the linear equation 𝑥 + 18 = 𝑥. State the property that justifies your first step and why you chose it.
1
1
2
4
1
4
1
5.
Solve the linear equation 17 − 𝑥 = ⋅ 15 + 6. State the property that justifies your first step and why you chose it.
6.
Solve the linear equation
7.
Sophia solved the linear equation 2𝑥 − 3 − 9𝑥 = 14 + 𝑥 − 1. Her work is shown below. When she checked her answer, the
left side of the equation did not equal the right side. Find and explain Sophia’s error, and then solve the equation correctly.
3
𝑥+𝑥+2
4
= 189.5. State the property that justifies your first step and why you chose it.
2𝑥 − 3 − 9𝑥 = 14 + 𝑥 − 1
−6𝑥 − 3 = 13 + 2𝑥
−6𝑥 − 3 + 3 = 13 + 3 + 2𝑥
−6𝑥 = 16 + 2𝑥
−6𝑥 + 2𝑥 = 16
−4𝑥 = 16
−4
16
𝑥=
−4
−4
𝑥 = −4