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http://www.mathslideshows.com
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What you do to one side of an equation, you must do to the other
side to keep it balanced.
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1) GOAL:Get the variable on one side of the equation.
2) You always perform the same operation toboth sides of an equation.
3) To undo an operation you perform its opposite operation to both sides of the equation.
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The inverse of add is SUBTRACT
The inverse of subtract is ADD
The inverse of multiply is
The inverse of divide is
DIVIDE
MULTIPLY
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x + 5 = -10 Get the variable alone.
- 5 - 5 Subtract 5 from both sides.
x = -15 +5 and -5 cancel each other out
-15 + 5 = -10 Check your answer
For an integer addition equation, subtract the same number from both sides
-10 = -10 Finish your check
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x + 8 = 2 -8 -8x = -6
y - 13 = -4 +13 +13
y = 9-6 + 8 = 2 2 = 2
9 – 13 = -4 -4 = -4
Try these!
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Try these!-3x = 21-3 -3
x = -7
m = 8-2(-2) (-2)
m = -16
-3(-7) = 21 21 = 21
= 8-2
-16
8 = 8
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Try these!1) -4 + x = 15 2) - 4 = m + 9
+4 +4x = 19
-9 -9-13 = m
- 4 + (19) = 15
15 = 15
- 4 = (-13) + 9
- 4 = - 4
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Try these!1) -5x = -35
-5 -5x = 7
-5(7) = -35
-35 = -35
2) 126
x
126
x
(-6)(-6)
-72 = x
122
6
7
12 = 12
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Try these!1) 8 y 3
8 8 y 5
8 + (-5) = 3
3 = 3
2) 9 m 3 3 3 6 m
- 9 = (-6) - 3
- 9 = - 9
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Try these!1) k 12
3
13 k 323
k 36
136
23
12 = 12
2) 8b 72
8b 28 8
7
b 9
-8(-9) = 72
72 = 72
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Try these!-4k = 14-4 -4
k 14
4
Acceptable Answers
k 7
2 35. 3
1
2
All answers must be fully reduced!
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Aren’t equationsinteresting?
TAKE OUT YOUR STUDY GUIDE
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a – -3 = 21 Get the variable alone.
+ -3 + -3 Add -3 to both sides.
a = 18 + -3 and – -3 cancel out
18 - -3 = 21 Check your answer
Use inverse operations to solve integer equations.
#7
Finish your check 21 = 21
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-8x = -64 Get the variable alone.
-8 -8 Divide -8 into both sides.
x = 8 -8 divided by -8 cancel out to 1.
-8 8 = -64 Check your answer.
Divide the same number into both sides
#8
Finish your check. -64 = -64
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1) -5 + x = 10 2) - 8 = m + 3+5 +5
x = 15-3 -3
-11 = m
- 5 + (15) = 10
10 = 10
- 8 = (-11) + 3
- 8 = - 8
Solve and Check
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1) -7x = -49-7 -7x = 7
-7(7) = -49
-49 = -49
2) 115
x
115
x
(-5)(-5)
-55 = x
115
5
5
11 = 11
Solve and Check
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1) 9 y 4 9 9
y 5
9 + (-5) = 4
4 = 4
2) 3 m 7 7 7 4 m
- 3 = (4) – 7
- 3 = - 3
Solve and Check
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1) k 108
18 k 808
k 80
180
08
10 = 10
2) 8b 72
8b 728 8
b 9
-8(-9) = 72
72 = 72
Solve and Check
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Solve the division by multiplying by the reciprocal.
1) 2)214
7y 7
2
7
2
14 7
1 2y
49y
216
7x
7
2
7
2
7 16
2 1x
56 x
8
11
7
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