Ch 1.7 (part 5) Variable on Both Sides
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Transcript of Ch 1.7 (part 5) Variable on Both Sides
![Page 1: Ch 1.7 (part 5) Variable on Both Sides](https://reader036.fdocuments.in/reader036/viewer/2022080917/5681303b550346895d95d439/html5/thumbnails/1.jpg)
Ch 1.7 (part 5)
Variable on Both Sides
Objective:
To solve equations where one variable exists on both sides of the equation.
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GOAL: Isolate the variable on one side of the equation.
1) Use the Distributive Property.(then simplify by combining LIKE Terms)
2) Choose one of the variable expressions and use the Inverse Property of Addition
3) Apply the Inverse Property of Addition and/or the Inverse Property of Multiplication to the numbers.
Perform Inverse operations to both sides of the equation!
Rules
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Special Cases
1) x = x
2) x + 1 = x
Plug in various numbers for x ……..
Plug in various numbers for x ……..
Solution: x = All Real Numbers
Solution: x = No solution
Every number makes a TRUE statement!
Every number makes a FALSE statement!
-x -x0 = 0
-x -x1 = 0
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-3 - 3
2x + 4 = 5x - 17
2x + 4 = 5x - 17 2x + 4 = 5x - 17-2x -2x
4 = 3x - 17+17 +17
21 = 3x3 3
7 = x
-5x -5x-3x + 4 = -17
-4 -4
-3x = -21
x = 7
Example 1
Option 1: Subtract 2x from both sides
Option 2: Subtract 5x from both sides
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4(x - 2) - 2x = 5(x - 4)4x - 8 - 2x = 5x - 20
2x - 8 = 5x - 20-2x -2x
-8 = 3x - 20+20 +20
12 = 3x3 3
€
x = 4
Example 2
Distributive Property
Combine LIKE Terms
Inverse Property of Addition for the variable
Inverse Property of Addition
Inverse Property of Multiplication
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3x + 8 = 2(x + 4) + x3x + 2 = 2(x - 1) + x3x + 8 = 2x + 8 + x3x + 8 = 3x + 8
-3x -3x
8 = 8
3x + 2 = 2x - 2 + x3x + 2 = 3x - 2
-3x -3x
2 = -2
x = any real number
True !False !
No Solution
Example 3 Example 4
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1) 3x - 5 = 2x + 12-2x -2x
x - 5 = 12+5 +5
x = 17
2) 5x - 3 = 13 – 3x+3x +3x8x - 3 = 13
+3 +38x = 168 8
x = 2
Classwork
3) 2b + 6 = 7b - 9-2b -2b
6 = 5b - 9+9 +915 = 5b 5 5
3 = b
4) -4c - 11 = 4c + 21+4c +4c
-11 = 8c + 21-21 -21-32 = 8c 8 8-4 = c
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5) 3(x + 2) - (2x - 4) = - (4x + 5)
3x + 6 - 2x + 4 = - 4x - 5 x + 10 = - 4x - 5
+ 4x + 4x
5x + 10 = -5- 10 -105x = -155 5
x = -3
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6) 4(y - 2) + 6y = 7(y - 8) - 3(10 - y)
4y - 8 + 6y = 7y - 56 - 30 + 3y
10y - 8 = 10y - 86
-10y -10y
-8 = -86 False
No Solution
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7) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19)
12 + 3k - 6k - 8 = 5k - 15 - 8k + 19
-3k + 4 = -3k + 4
+3k +3k
4 = 4 True
Infinitely Many Solutions!
x = all real numbers
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8) 5(m - 4) = 10 - 4[2(m - 5) - 5m]
5m - 20 = 10 - 4[2m - 10 - 5m]
5m - 20 = 10 - 4[-3m - 10]
5m - 20 = 10 + 12m + 40
5m - 20 = 12m + 50-5m -5m
-20 = 7m + 50-50 -50-70 = 7m
7 7
x = -10