Download One Step Equations

One Step Equations
To undo addition, subtract the number from both sides of the equal sign
Ex: x + 4 = 9
10 = r + 6
-4 -4
-6
-6
x = 5
4 = r
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To undo subtraction, add the number to both sides of the equal sign
Ex: x – 7 = 12
-5 = r – 2
-8 + x = 12
+7 +7
+2
+2
+8
+8
x = 19
-3 = r
x = 20
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To undo multiplication, divide the number on both sides
Ex: 3x = 9
3
3
-48 = -6x
-6
-6
x=3
8=x
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To undo division, multiply the number on both sides of the equal sign
Ex: x = 9
4
-2 = a
7
x =9 (4)
-2(7) = a
x = 36
-14 = a
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To undo fractions: multiply both sides by the denominator. Then divide by the coefficient of the variable.
Ex:
2
x 8
3
4
x 8
5
Try these:
1) x + 6 = -5
2) 4 = x – 7
3) -9 + x = 10
5) -7x = 42
6) 40 = 5x
7)
7
x7
4
4) -8 = x – 7
8)
2
x6
5
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Two Step Equations:
Step 1: Undo addition and subtraction
Step 2: Undo multiplication and division
Ex: 1) 2x – 4 = 10
+4 +4
3) –n + 5 = -7
-5 -5
2) 9 + 3x = 24
-9
-9
2x = 14
3x = 15
-n
2x = 14
2
2
3x = 15
3
3
-1n
-1
x=7
x=5
= -12
= -12
-1
n = 12
4) 8 = x + 6
4
-6
-6
2=x
4
(4)2 = x(4)
4
8=x
Try these:
1) 7x – 3 = 11
2) –x + 8 = -3
3) 4 – 5x = 34
4)
x
 3  1
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Combining Like Terms
To combine like terms, you must combine like terms on each side of the equal sign.
Examples:
1) 9x – 2 – 7x = 18
so, 2x – 2 = 18
+2 +2
so, 2x = 20
2
2
Combine 9x – 7x = 2x, then bring everything else down
Then undo subtraction
Then undo multiplication
so, x = 10
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2) 8x + 12 – 28 = -64
Combine 12 – 28 = -16, bring everything else down
so, 8x – 16 = -64
+ 16 +16
Then undo subtraction
so, 8x = -48
8
8
Then undo multiplication
so, x = -6
Try these:
1) 7x – 5x + 4 = 26
2) 24 + 3x – 6 = 9
3) 10 = -7x + 25 + 2x
Distributing
To distribute, multiply the number in front of the parenthesis to each of the terms inside the parenthesis
Examples: Distribute
1) 3(x – 4)
(Multiply 3 times x, and multiply 3 times -4)
2) -6(3x – 4)
3x – 12
-18x + 24
Solve the following:
3) 6(x + 5) = -54
4) -2(4x + 8) = 24
5) -8(3x + 6) + 22x = 32
so, 6x + 30 = -54
-30 - 30
so, -8x – 16 = 24
+ 16 +16
so, -24x – 48 + 22x = 32
so, 6x = -84
6
6
so, -8x = 40
-8
-8
so, x = -14
so, x = -5
so, -2x – 48 = 32
+ 48 +48
so, -2x = 80
-2
-2
so, x = -40
Try these:
1) 5(x – 7) = 30
2) -3(x – 6) = 12
3) -7(2x + 2) + 42 = 28
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Variables on Both Sides
When there are variable on both sides of the equal sign,
then move the smaller variable by adding or subtracting its opposite
Example:
1) 5x + 9 = 3x – 7
-3x
-3x
2) -6x – 8 = 2x + 16
+6x
+6x
Subtract the smaller variable
2x + 9 = -7
- 9 -9
-8 = 8x + 16
-16
- 16
2x = -16
2
2
- 24 = 8x
8
8
x = -8
-3 = x
Try these:
1) 7x + 10 = 5x – 22
2) 3x + 14 = -4x – 28
Multi-step Equations
Example:
10 – 2(4x +12) = -6x + 4
1) If there are parentheses present, then distribute
10 – 8x – 24 = -6x + 4
2) Combine like terms on each side of the equal sign
-8x – 14 = -6x + 4
+8x
+8x
3) If there are variables (letters) on both sides,
then move the smaller variable by adding or
subtracting its opposite.
4) Undo addition or subtraction
-14 = 2x + 4
-4
-4
-18 = 2x
2
2
5) Undo multiplication or division
-9 = x
48
Name: ____________________
Solve the following:
1) 60 = 12b
2) -9n = -36
3) x + 5 = -2
4) x – 8 = 12
5) 4 + x = 2
6) a/2 = 4
7) 13 = x – 8
8) 10 = -5x
9) 3x + 12 = 18
10) 15 + 4a = -1
11) 7 = -2p + 13
12) -8 = 3h – 8
13) 3f – 12 = -15
14) 2f + 30 = 28
15) -5 = 15 – 10b
16) n + 7 = 5
17) 25 = -5x + 15
18) 3x – 9 = -27
19) 16 = -4x + 20
20) ¼ x + 6 = 10
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Two Step Equations
Name:________________________
SHOW ALL WORK
= -5
3) 9x – 7 = 20
4) 0 = 4 + 2n
5) -9x + 1 = -80
6) 10 + 3n = 46
7) 8 – 5x = 38
8) 2x – 7 = -15
9) –m + 3 = 11
10) 8x – 2 = -26
11)
13) -10 = -10 + 7m
14) -15 = -4g + 5
15) 7 + 3x = 28
1) 6 =
+2
2) -6 +
–1 =4
12) 11 = -6r – 31
16) 4x – 8 = 24
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Practice Solving Equations
Combining like terms
Distributing
Name: _____________________
Date: ________ Period: _______
Combine like terms:
1) 8x + 2y – 4x + 3y
2) 6x2 – 3x + 4x – 2x2
3) 5a + 7 – 4a
4) 7x2 + 8 – 3x + 2
Solve:
5) 12x + 8 – 8x = 44
6) 19 – 2x + 17 = 6
7) -3 = 7x + 24 – 4x
8) 15 = -5x + 22 – 32
Distribute
9) -5(x + 6)
10) 3(-5x + 8)
11) -4(7x – 10)
Solve:
12) 3(x + 8) = -36
13) -4(2x – 8) = 72
14) 42 = 7(-x + 4)
15) -2(x + 9) – 20 = 10
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Name: _____________________
Algebra Practice Solving Equations
Date: ______________
READ ALL DIRECTIONS CAREFULLY
Solve the following equations:
1) g – 4 = 7
2) -3t = 9
3) 8 + x = 12
4) x = 9
3
5) 4a + 6 = 14
7) -2a – 6 = -68
8) x – 7 = 4
2
6) 39 = -3x + 3
Simplify each expression:
9) 5p + 7e – 4p + 5e
10) -7h – 4 + 5h – 9
11) 8x + 4x – 9y + 10y
Solve the following equations:
12) 5n + 6n = 77
13) 2t + 8 – t = -3
14) x + 24 – 9x = -8
Simplify the following expressions:
15) 2(x + 9)
16) -5(2e + 4)
17) -1(3k – 1)
Solve the following equations:
18) 5(2 – x) = 5
19) 2(a – 1) = 42
20) -7(2a – 6) = 112
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Solving Equations Practice Quiz
Like Terms/Distribute/Variable on both sides
Name: _____________________
Date: ________ Period: _______
Solve the following equations:
1) 8 = 7x – 3x
2) 50 – 12 = -7x + 5x
3) x + 3x = -20
4) 7x + 4(x – 11) = -22
5) -5(x + 7) = 20
6) 2x + 9 – 5x = -27
7) 58 = 3(4x + 9)
8) 14 = 8x + 49 – x
9) 9x + 8 = -2x + 52
10) 15x – 22 + 4 = 12
11) -7x + 5 = 2x – 31
12) 4x + 5x – 33 = 6x – 9
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Multi-step Equation Practice
Multi-step Equations
Example:
10 – 2(4x +12) = -x + 4
1) If there are parentheses present, then distribute
10 – 8x – 24 = -6x + 4
2) Combine like terms on each side of the equal sign
-8x – 14 = -6x + 4
+8x
+8x
3) If there are variables (letters) on both sides,
then move the smaller variable by adding or
subtracting its opposite.
4) Undo addition or subtraction
-14 = 2x + 4
-4
-4
-18 = 2x
2
2
5) Undo multiplication or division
-9 = x
1) 4x + 9 = 2x + 6
2) –x – 2 = 3x + 5
3) 2 – 5(z + 1) = 3z + 1
4) 9x – 12 = 8x – 3
5) c – 12 = 3c + 12
6) 4y + 3(2y – 4) = y + 6
7) 5a + 3 – 2a = 7
8) 20 – x = 19 + 2x
9) 8x – 1 = 23 – 4x
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10) 5 + 4x – 7 = 4x – 2 – x
11) 9 = 3(5x – 2)
12) 6x – 1(3x + 8) = 16
13) 7(5x – 2) = 6(6x – 1)
14) 2n + 3n + 7 = -41
15) 3h – 5h + 11 = 17
16) 2t + 8 – t = -3
17) -6 – 3(2d + 4) = 18
18) 2b – 6 + 3b = 14
19) 2(a – 4) + 15 = 13
20) 7 + 2(a – 3) = -9
21) -4d + 2(3 + d) = -14
22) 13 + 2(5c – 2) = 29
23)3c – 8c + 7 = -18
24) 6a – 2a = -36
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25) -4x + 3(2x – 5) = 31
26) –w + 4(w + 3) = -12
27)2(3a + 2) = -8
28) 5(t – 3) – 2t = -30
29) 3(t – 12) = 27
30) 4x + 9 = 7x – 12
31) 2(m + 1) = 16
32) 3(x + 6) = 5(x – 4)
34) 24y – 2(6 – y) = 6(3y + 2)
35) 4(m + 3) – 2m = 3(m – 3)
37) 4 + 5(3 – x) = 32 + 8x
38)10y = 2y – 6y + 7
33) 5(x + 2) = x + 6(x – 3)
36) -3g + 9 = 15g – 9
39) 8x – 3x + 4 = 3x + 8
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Multi-step Equations Practice
Solve (One and Two-step Equations)
1) 6x = 24
2) x + 7 = 13
6) c = -3
7
11) 2n – 14 = 24
7) 39 + x = -2
12) 6x + 24 = -6
16) a + 5 = -10
2
Combine like terms:
21) 2x + 11y – 12x + 4y
17) 8 = 3 – m
4
Name: _____________________
Date: ________ Period: _______
3) 13 = a – 4
4) -5 + m = 20
10) x – 6 = -11
8) 4 = x
-3
9) 54 = -9x
13) -24 + 3d = 9
14) 24 = -8x + 8
18) 16 – a = 4
22) 7x2 – 5x + 9x – 2x2
5) -7x = 28
15) –c + 12 = 3
19) 10x + 25 = -35 20) -11e + 5 = 49
23) 10a + 5 – 3a
24) 6x – 4y + 3x – 2x
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Solve:
25) 8n + 3n = 66
26) –a + 6a = -55
Distribute
29) -3(9 - x)
30) -2(4c – 8) 41) -5(7x – 12)
Solve:
32) 2(a + 8) = -10
33) 5(3d – 7) = 10
Variables on both sides:
36) 9x + 42 = 7x + 4
Solve (Five-step Equations)
39) 30 + 4(x – 7) = 6x – 12
27) 4x – 10 + 2 = 40
28) -4 = 7g + 10 – 5g
31) -9(x + 7) – 3x
34) -4(2x – 9) + 6x = 2
37) 6x + 30 = 9x – 9
35) 5 + 5(c + 3) = 45
38) -2x – 24 = 4x + 54
40) -5(x + 4) = 12x – 7x + 30
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Word Problems
1) Alexis’s mom gave her $20 to go to the movie theater. Her ticket cost $8. Candy is $4 each.
A) Write an equation to represent the situation
B) Solve the equation to find out how many boxes of candy can Alexis buy?
2) You have $50 to buy Christmas presents for your family. You plan on spending 22 for your sibling, and
you want to buy your mom and day as many passes to the movie theater as you can with the rest of the
money. The movie tickets cost $8.
A) Write an equation to represent the situation
B) Solve the equation to find out how many tickets you can buy your parents?
3) It cost $8 to rent ice skates and $4 for each hour you skate. You have $30.
A) Write an equation to represent the situation
B) Solve the equation to find out how many hours you can go ice skating.
4) Erica makes $7.50 an hour. She also received a $100 bonus for being employee of the month. She made
$37 in overtime for the month. She made $377 this month.
A) Write an equation to represent the situation
B) Solve the equation to find out how many hours Erica worked.
5) Alissa’s homecoming dress cost $120. She put down $60 for the dress and paid $15 each month.
A) Write an equation to represent the situation
B) Solve the equation to find out how many months it took her to pay off the
dress.
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Special Solutions for Solving Equations
When the variable are eliminated:
1) Get a solution where a number = itself
Ex 7 = 7
- This is called an identity
- This means that there is infinite solutions
Ex: 2x – 7 + 4 = 2x – 3
Combine like terms
2x – 3 = 2x – 3
- 2x
- 2x
-3 = -3
Variables on both sides
The equations is an identity
OR
2) Get a solution where a number = another number Ex: 5 = 8
- This means that there are no solutions
EX:
3(x – 4) = 3x + 10
Distribute
3x – 12 = 3x + 10
-3x
-3x
-12 = 10
1) 5x + 17 = 4 + 5x
Variables on both sides
The equation has no solution
2) 3(x + 4) = 5x – 2x + 12
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Special Solutions Practice
Solve each equation.
There are 3 possible outcomes:
1) Solution (ex: x = 5)
2) Identity
3) No solution
1) -20 = -4x – 6x
2) 2p + 10 = 10 + 2p
4) 5x – 3x = 2x + 7
5) 8x – 20 = 2(4x – 10)
7) -(y + 11) = 15
8) -12x + 10x – 9 = -2x + 9
3) 14n + 32 = -2(-7n + 3)
6) 5(x – 7) + 20 = 2x + 3x – 4
9) 7x + 11+ 10 = 7(x + 3)
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