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Name: ____________________________
Mr. Art
Date: ________________
Period: _______________
Solving Linear Equations
One-Step Equations (one operation)
 use inverse operations
1) 3x = 12
2) b – 9 = -14
3) a + 7 = 10
4)
t
5
20
Two-Step Equations (two operations)
 Goal: Get the variable by itself
 First, work with the terms that do not have a variable (constant before coefficient)
1) 3y + 7 = 22
2)
3) 23 – 5y = 11
m
 6  11.5
4
4) 52x – 213 = -57
Equations with parentheses – Distributive Property
 Use the distributive property to remove parentheses
 Then, use inverse operations to solve
1) 3(x + 2) = 21
2) 15 = -8(y + 4)
3) 4(3 – m) = -22
4) -2(3x – 2) = -10
Combining like terms
 Combine like terms that are on the same side of the equal sign
 Then, use inverse operations to solve
1) 3x + 4x = 28
2) 9x = 17 – 62
3) 8x – 2 + 3x + 7 = 27
4) 2y + 7 – 5y = 2.5 – 3
Variables on both sides of the equal sign
 Use inverse operations to get the variables all on one side of the equation
(You cannot combine variables on different sides of the equal sign!)
 Then, use inverse operations
1) 2x + 17 = 3x
2) 5x = -10 + 3x
3) 12x = 10 – 8x
4) 8x – 10 = -30 + 3x
Multi-Strategy Problems (more than one strategy)
 First, remove parentheses.
 Second, combine like terms
 Third, move all variables to one side of the equals sign
 Last, use inverse operations to isolate the variable.
1) 8 + 3(x + 7) = 4x
2) 2x – 3(x – 5) = 7x + 7