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Algebra 1
Section 3.2
Solving Equations Using Two
or More Transformations
To solve an equation involving two or more steps: Remember: your main
goal in life, at this point, is to get the x (variable) to one side and by itself,
while clearing away everything else to the other side.
{Always keep in mind: whatever you do to one side, you have to do
to the other side.}
3x + 2 = 8
-2
-2 subtract 2 from both sides
3x = 6
x=2
divide both sides by 3
1 + 6 = -8
3x
-6
-6 subtract 6 from both sides
1 = -14
3x
x = - 42
multiply both sides by 3
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7x – 3x – 8 = 24
4x – 8 = 24
+8
combine like terms
+8 add 8 to both sides
4x = 32
x=8
divide by 4
5x + 3(x + 4) = 28
5x + 3x + 12 = 28
8x + 12 = 28
-12 -12
8x = 16
x=2
18 – (x + 2) = 21
18 – x – 2 = 21
-x + 16 = 21
distributive property
combine like terms
subtract 12 from both sides
divide by 8
take the negative of everything in parentheses
combine like terms
-16 -16 subtract 16 from both sides
-x = 5
x = -5
divide both sides by -1
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Solve each equation.
1. 3x – 7 = 23
+7 +7 add 7 to both sides
3x = 30
x = 10
divide both sides by 3
3. 6 = 14 – 2x
-14 -14 subtract 14 from both sides
-8 = -2x
x = 4 divide both sides by -2
2. 1 + 2 = 3
4x -2 -2
1 = 1
4x
x=4
subtract 2 from both sides
multiply both sides by 4
4. - 4 + 4 = -6
5x +4
+4
add 4 to both sides
4 = -2
5x
x = -2 ½
multiply both sides by 5/4
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5. 4x + 5 = -3
3
-5
-5
subtract 5 from both sides
6. 4x – 3x = 9
x = 9 combine like terms
4x = -8
3
x=-6
multiply both sides by ¾
7. x + 5x – 5 = 1
6x – 5 = 1
combine like terms
+5 +5 add 5 to both sides
6x = 6
x=1
divide both sides by 6
8. -2 = 2x - x
3
-2 = 2x - 3x
3
3 common denominator
-2 = -x
3
x=6
combine like terms
multiply both sides by -3
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9. 3(x – 2) = 18
10. 19 = 2(x + 1) – x
3x – 6 = 18 distributive property
19 = 2x + 2 – x distributive property
+6 +6 add 6 to both sides
19 = x + 2 combine like terms
3x = 24
-2
-2 subtract 2 from both sides
x = 8 divide both sides by 3
x = 17
11. 3x + 3 (2x – 1) = 2
12. 9 (x + 3) = 27
2
2
3x + 3x – 3/2 = 2 distributive property
9 + 27 = 27
6x – 3/2 = 2 combine like terms
2x 2
+3/2 +3/2 add 3/2 to both sides
6x = 7/2
x = 7/12
divide by 6 {multiply by 1/6}
-27/2
distributive prop.
-27/2
9 = 27
2x 2
x=3
multiply both sides by 2/9
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13. The bill (parts and labor) for the repair of an automobile was $357.
The cost for parts was $285. The cost of labor was $32 an hour.
Let x represent the number of hours of labor. Write an equation
involving x and solve the equation to find the number of hours of
labor.
labor/hr  hours of labor + parts = total
$32

x
+ $285 = $357
32x + 285 = 357
-285
-285
32x = 72
x = 2 ¼ hours
© Mr. Sims
Solve each equation.
1.) 2x + 5 = 9
4.) 3x 
1
 1
2
7.) 3x – 7 + x = 5
10.) 6 
12.)
3
1
x  (x  4)
2
2
2
x  1
3
2.) 1 x  1   1
2
3.) 9 
5.) 16  2  2x
5
6.) - 6x + 4x = 2
8.)  10 
1
xx
2
Algebra 1
Section 3.2
Assignment
9.) 12(2 – x) = 6
11.) 55x – 3(9x + 12) = - 64
4
(2x  4)  48
9
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