Combining Like Terms to Solve Equations Tutorial 6c.
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Transcript of Combining Like Terms to Solve Equations Tutorial 6c.
![Page 1: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/1.jpg)
Combining Like Termsto Solve Equations
Tutorial 6c
![Page 2: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/2.jpg)
Definitions
An equation is created when two mathematical expressions, that are made up of terms, are set equal to one another. 3x – 12 = 7x + 2
A term is a number or a variable, or the product or quotient of numbers and variables. 3x, 12, 7x, and 2 are all terms in the above
equation
If a term has a variable, the numerical factor is called the coefficient. 3 and 7 are coefficients
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Identifying Coefficients
To identify the coefficients of each term in the expression –x + 7y + 4, you can write the expression as –1x + 7y + 4.
–1x +7y + 4
3 terms3 terms3 terms3 terms3 terms3 terms3 terms
Coefficients
–1 7
Constant
4
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Like Terms
Terms are like terms if they meet two criteria: The terms must have the same
variable(s).
The variable(s) must have the same exponents on them.
4x and 11x2 are not like terms. They do not have the same exponent.5x and 7x are like terms. They meet both criteria above.
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Example #1
You can combine like terms by adding the coefficients. Simplify: 3x + 8 + 5x – 2
3x + 5x 8 – 2 Then add or subtract. 8x 6
The simplified expression is 8x + 6.
Terms with x Constant terms Group like terms
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Example #2
Simplify: -2 + 6x + z – 2x + 8 – 4z
Terms with x Terms with z Constant terms Group like terms
6x - 2x 1z – 4z -2 + 8 Then add or subtract. 4x -3z 6
The simplified expression is 4x – 3z + 6.
![Page 7: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/7.jpg)
Solving EquationsSolve and then check your answer: 7x – 3x – 6 = 6
To undo the subtraction, add a 6 to each side of the equation.
Always check your answers! 7x – 3x – 6 = 6; Does x =3?7•3 – 3•3 – 6 = 6 is true!
4x – 6 = 6
x = 3
4 4
1 3
1 1
4x = 12 To undo the multiplication, divide by 4 on each side of the equation.
x is now all alone on one side of the equation!
Combine like terms. 7x – 3x – 6 = 6
+ 6 + 6
![Page 8: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/8.jpg)
Problem SolvingAs a gift for your brother, you order concert tickets. Two days before the concert a friend asks to join you. When you order the third ticket, there is a $12 charge for express delivery to be sure the ticket arrives on time. The total bill is $78. How much does each person (yourself and your friend) owe?
Define your variable: Let c = charge for each original ticket.
Let c + 12 = total charge for the late ticket.
Relate:
Charge for theoriginal 2 tickets
plus Total charge forthe late ticket
is 78
Write: 2c + C + 12 = 78
Solve: 2c + c + 12 = 78
![Page 9: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/9.jpg)
Problem SolvingAs a gift for your brother, you order concert tickets. Two days before the concert a friend asks to join you. When you order the third ticket, there is a $12 charge for express delivery to be sure the ticket arrives on time. The total bill is $78. How much does each person (yourself and your friend) owe?
To undo the addition, subtract a 12 from each side of the equation.
Always check your answers!$44 + $34 = $78
3c + 12 = 78
c = 22
3 3
1 22
1 1
3c = 66 To undo the multiplication, divide by 3 on each side of the equation.
Combine like terms. 2c + c + 12 = 78
- 12 -12
You owe 2•($22) = $44Your friend owes $22 + $12 = $34
Let c = charge for each original ticket.Let c + 12 = total charge for the late ticket.
![Page 10: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/10.jpg)
Distributive Property
For all real numbers a, b, c:a(b + c) = ab + ac (b + c)a = ba + caa(b – c) = ab – ac (b – c)a = ba – ca
Examples:
3(2x + 5) = 3(2x) + 3(5) = 6x + 15
(5b – 6)4 = (5b)4 – (6)4 = 20b – 24
![Page 11: Combining Like Terms to Solve Equations Tutorial 6c.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649ce45503460f949b0a47/html5/thumbnails/11.jpg)
Solving EquationsSolve and then check your answer: 6x + 12(10 – x) = 84
To undo the addition, subtract a 120 to each side of the equation.
Always check your answers! 6x + 12(10 – x) = 84; Does x =6?6•6 + 12(10 – 6) = 84 is true!
-6x + 120 = 84
x = 6-6 -6
1 6
1 1
-6x = -36 To undo the multiplication, divide by -6 on each side of the equation.
Combine like terms.
6x + 12 (10 – x) = 84
-120 -120
Distribute. 6x + 12•(10) – 12x = 84
6x + 120 – 12x = 84
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