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![Page 1: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/1.jpg)
An equation is a mathematical statement that two expressions are equal.
A solution of an equation is a value of the variable that makes the equation true.
To find solutions, isolate the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.
![Page 2: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/2.jpg)
Inverse Operations
Operation Inverse Operation
Addition Subtraction
Subtraction Addition
Isolate a variable by using inverse operations which "undo" operations on the variable.
An equation is like a balanced scale. To keep the balance, perform the same operation on both sides.
![Page 3: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/3.jpg)
Inverse Operations
Operation Inverse Operation
Multiplication Division
Division Multiplication
Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable.
![Page 4: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/4.jpg)
Solve the equation. Check your answer.
Since 8 is subtracted from y, add 8 to both sides to undo the subtraction.
y – 8 = 24 + 8 + 8
y = 32
Check y – 8 = 24
32 – 8 2424 24
To check your solution, substitute 32 for y in the original equation.
![Page 5: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/5.jpg)
Solve the equation. Check your answer.
= z34
To check your solution, substitute for z in the original equation.
34
+ 716
+ 716
= z – 716
516
Check= z – 7
16 516
34
516
716
–
516
516
Since is subtracted from z, add to
both sides to undo the subtraction.
716
716
![Page 6: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/6.jpg)
Solve the equation. Check your answer.
Whiteboards
n – 3.2 = 5.6
![Page 7: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/7.jpg)
Solve the equation. Check your answer.
Whiteboards
–6 = k – 6
![Page 8: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/8.jpg)
Solve the equation. Check your answer.
Whiteboards
16 = m – 9
![Page 9: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/9.jpg)
Solve the equation. Check your answer.
Whiteboards
–13 =y3
![Page 10: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/10.jpg)
Solve the equation. Check your answer.
Since 17 is added to m, subtract 17 from both sides to undo the addition.
m + 17 = 33– 17 –17
m = 16
Check m + 17 = 33
16 + 17 3333 33
To check your solution, substitute 16 for m in the original equation.
![Page 11: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/11.jpg)
Solve the equation. Check your answer.
Since 1.8 is added to t, subtract 1.8 from both sides to undo the addition.
4.2 = t + 1.8 –1.8 – 1.8
2.4 = t
Check 4.2 = t + 1.8
4.2 2.4 + 1.84.2 4.2
To check your solution, substitute 2.4 for t in the original equation.
![Page 12: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/12.jpg)
Solve the equation. Check your answer.
Whiteboards
d + = 1 1 2
![Page 13: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/13.jpg)
Solve the equation. Check your answer.
Whiteboards
–5 = k + 5
![Page 14: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/14.jpg)
Solve the equation. Check your answer.
Whiteboards
6 + t = 14
![Page 15: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/15.jpg)
Remember that subtracting is the same as adding the opposite. When solving equations, you will sometimes find it easier to add an opposite to both sides instead of subtracting.
![Page 16: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/16.jpg)
p = 311
+ 511
+ 511
Solve – + p = – . 211
511
511
Since – is added to p, add to both sides.
511
Check + p = – 211
511
–
2 511 11
– – 311
+
211
– 211
–
To check your solution, substitute for p in the original equation.
311
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Solve –2.3 + m = 7. Check your answer.
Whiteboards
–2.3 + m = 7
![Page 18: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/18.jpg)
Whiteboards
Solve – + z = . Check your answer. 5 4
3 4
– + z =
5 4
3 4
![Page 19: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/19.jpg)
Solve the equation. Check your answer.
Whiteboards
–13 =y3
![Page 20: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/20.jpg)
Solve –11 + x = 33. Check your answer.
–11 + x = 33
![Page 21: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/21.jpg)
Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.
![Page 22: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/22.jpg)
Solve the equation.
w = 24
20 20
To check your solution, substitute 24 for w in the original equation.
w = 2056
Check w = 2056
The reciprocal of is . Since
w is multiplied by , multiply
both sides
by .
56
65
566
5
20
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Solve the equation. Check your answer.Whiteboards
– = b14
15
![Page 24: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/24.jpg)
WhiteboardsSolve the equation.
=4j6
23
![Page 25: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/25.jpg)
w = 10216
Solve the equation.Whiteboards
![Page 26: An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true.](https://reader037.fdocuments.net/reader037/viewer/2022102722/551c2d6f5503469e4f8b618f/html5/thumbnails/26.jpg)
Over 20 years, the population of a town decreased by 275 people to a population of 850. Write and solve an equation to find the original population.
Example 4: Application
Write an equation to represent the relationship.
+ 275 + 275
p =1125
p – d = c
original population minus
current population
decrease in
populationis
p – 275 = 850 Since 275 is subtracted from p, add 275 to both sides to undo the subtraction.
p – d = c
The original population was 1125 people.