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Co
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NAME ___________________________________________________ DATE _____________________ PERIOD __________
Lesson 2 ReteachSolving Two-Step Equations
Example 1 Solve 1 − 2 c - 13 = 7. Check your solution.
1 − 2 c - 13 = 7 Write the equation.
1 − 2 c - 13 + 13 = 7 + 13 Addition Property of Equality
1 − 2 c = 20 Simplify.
2 � 1 − 2 c = 2 � 20 Multiplication Property of Equality
c = 40 Simplify. Check your solution.
Example 2 Solve 7y - 2y + 4 = 29. Check your solution.
7y - 2y + 4 = 29 Write the equation. Check 7y - 2y + 4 = 29 5y + 4 = 29 Combine like terms. 7(5) - 2(5) + 4 � 29 -4 = -4 Subtraction Property of Equality 35 - 10 + 4 � 29 5y = 25 Simplify. 25 + 4 � 29
5y
− 5 = 25 − 5 Division Property of Equality 29 = 29 �
y = 5 Simplify. Check your solution.
Exercises Solve each equation. Check your solutions. 1. 5t + 2 = 7 2. 2x + 5 = 9 3. 6.2u - 8 = 29.2
4. 8m - 7 = 17 5. 1 − 7 m - 9 = 5 6. 1 − 9 k - 3 = - 11
7. 13 + 1 − 4 a = -3 8. -3 + 1 − 2 c = 12 9. 7 - h = 209
10. -g + 18 = -32 11. 16.4 - p = 3.5 12. - 2 − 5 c - 8 = 32
13. 3 − 8 q + 12 = 36 14. 3 - 3 − 4 n = 9 15. 7 − 9 v + 2 = 23
A two-step equation contains two operations. To solve two-step equations, use inverse operations to undo each operation in reverse order of the order of operations. First, undo addition/subtraction. Then, undo multiplication/division.
Check 1 − 2 c - 13 = 7
1 − 2 (40) - 13 � 7
20 - 13 � 7
7 = 7 �
Math Accelerated • Chapter 8 Equations and Inequalities
Program: Pre-Algebra
Vendor: Aptara
Component: ANC_C08_L2
Grade: AMPDF Pages
006_010_AM_ANC_C08_L2_664489.indd Page 6 25/07/12 2:44 AM s-019006_010_AM_ANC_C08_L2_664489.indd Page 6 25/07/12 2:44 AM s-019 /Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES.../Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES...
Co
py
righ
t © T
he
McG
raw
-Hill C
om
pa
nie
s, Inc. P
erm
ission
is gra
nte
d to
rep
rod
uce
for cla
ssroo
m u
se.
NAME ___________________________________________________ DATE _____________________ PERIOD __________
Lesson 2 ReteachSolving Two-Step Equations
Example 1 Solve 1 − 2 c - 13 = 7. Check your solution.
1 − 2 c - 13 = 7 Write the equation.
1 − 2 c - 13 + 13 = 7 + 13 Addition Property of Equality
1 − 2 c = 20 Simplify.
2 � 1 − 2 c = 2 � 20 Multiplication Property of Equality
c = 40 Simplify. Check your solution.
Example 2 Solve 7y - 2y + 4 = 29. Check your solution.
7y - 2y + 4 = 29 Write the equation. Check 7y - 2y + 4 = 29 5y + 4 = 29 Combine like terms. 7(5) - 2(5) + 4 � 29 -4 = -4 Subtraction Property of Equality 35 - 10 + 4 � 29 5y = 25 Simplify. 25 + 4 � 29
5y
− 5 = 25 − 5 Division Property of Equality 29 = 29 �
y = 5 Simplify. Check your solution.
Exercises Solve each equation. Check your solutions. 1. 5t + 2 = 7 2. 2x + 5 = 9 3. 6.2u - 8 = 29.2
4. 8m - 7 = 17 5. 1 − 7 m - 9 = 5 6. 1 − 9 k - 3 = - 11
7. 13 + 1 − 4 a = -3 8. -3 + 1 − 2 c = 12 9. 7 - h = 209
10. -g + 18 = -32 11. 16.4 - p = 3.5 12. - 2 − 5 c - 8 = 32
13. 3 − 8 q + 12 = 36 14. 3 - 3 − 4 n = 9 15. 7 − 9 v + 2 = 23
A two-step equation contains two operations. To solve two-step equations, use inverse operations to undo each operation in reverse order of the order of operations. First, undo addition/subtraction. Then, undo multiplication/division.
Check 1 − 2 c - 13 = 7
1 − 2 (40) - 13 � 7
20 - 13 � 7
7 = 7 �
1 2 6
3 98 -72
-64 30 -202
50 12.9 -100
64 -8 27
Math Accelerated • Chapter 8 Equations and Inequalities
Program: Pre-Algebra
Vendor: Aptara
Component: ANC_C08_L2
Grade: AMPDF Pages
006_010_AM_ANC_C08_L2_664489.indd Page 6 25/07/12 2:44 AM s-019006_010_AM_ANC_C08_L2_664489.indd Page 6 25/07/12 2:44 AM s-019 /Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES.../Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES...
Co
py
righ
t © T
he
McG
raw
-Hill C
om
pa
nie
s, Inc. P
erm
ission
is gra
nte
d to
rep
rod
uce
for cla
ssroo
m u
se.
NAME ___________________________________________________ DATE _____________________ PERIOD __________
Lesson 4 ReteachMore Two-Step Equations
Example 1 Solve the equation -3(x + 4) = 27.-3(x + 4) = 27 Write the equation.
-3(x + 4)
− -3 =
27 − -3 Division Property of Equality
x + 4 = -9 Simplify.
x + 4 - 4 = -9 - 4 Subtraction Property of Equality
x = -13 Simplify.
Example 2 Solve 2(d -10) = -6.2(d - 10) = -6 Write the equation.
2d - 20 = -6 Distributive Property
2d - 20 + 20 = -6 + 20 Addition Property of Equality
2d = 14 Simplify.
2d − 2 = 14 − 2 Division Property of Equality
d = 7 Simplify.
Exercises Solve each equation.
1. 2(y + 7) = 20 2. -4(v - 1) = 16 3. 39 = 13(x - 8)
4. 99 = 11(q + 4) 5. 3 − 4 (n - 3) = 18 6. 4 − 9 (p + 8) = -20
7. 36 = 3 − 8 (k - 5) 8. 1 − 2 (c + 2) = 5 9. 0.2(g + 12) = 50
10. -2.7(a + 9) = 13.5 11. 2(b - 13) = 15 12. -6(d + 14) = -57
Solving equations of the form p(x + q) = r, can be accomplished in one of two ways:
1. When p is a factor of the constant term, r, then:
• use the Division Property of Equality when p is a whole number or decimal.
• use the Multiplication Property of Equality when p is a fraction.
2. Regardless if p is or is not a factor of the constant term, r, you can use the Distributive Property.
Program: Pre-Algebra
Vendor: Aptara
Component: ANC_C08_L4
Grade: AMPDF Pages
Math Accelerated • Chapter 8 Equations and Inequalities
016_020_AM_ANC_C08_L4_664489.indd Page 16 25/07/12 2:43 AM s-019016_020_AM_ANC_C08_L4_664489.indd Page 16 25/07/12 2:43 AM s-019 /Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES.../Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES...
Co
py
righ
t © T
he
McG
raw
-Hill C
om
pa
nie
s, Inc. P
erm
ission
is gra
nte
d to
rep
rod
uce
for cla
ssroo
m u
se.
NAME ___________________________________________________ DATE _____________________ PERIOD __________
Lesson 4 ReteachMore Two-Step Equations
Example 1 Solve the equation -3(x + 4) = 27.-3(x + 4) = 27 Write the equation.
-3(x + 4)
− -3 =
27 − -3 Division Property of Equality
x + 4 = -9 Simplify.
x + 4 - 4 = -9 - 4 Subtraction Property of Equality
x = -13 Simplify.
Example 2 Solve 2(d -10) = -6.2(d - 10) = -6 Write the equation.
2d - 20 = -6 Distributive Property
2d - 20 + 20 = -6 + 20 Addition Property of Equality
2d = 14 Simplify.
2d − 2 = 14 − 2 Division Property of Equality
d = 7 Simplify.
Exercises Solve each equation.
1. 2(y + 7) = 20 2. -4(v - 1) = 16 3. 39 = 13(x - 8)
4. 99 = 11(q + 4) 5. 3 − 4 (n - 3) = 18 6. 4 − 9 (p + 8) = -20
7. 36 = 3 − 8 (k - 5) 8. 1 − 2 (c + 2) = 5 9. 0.2(g + 12) = 50
10. -2.7(a + 9) = 13.5 11. 2(b - 13) = 15 12. -6(d + 14) = -57
Solving equations of the form p(x + q) = r, can be accomplished in one of two ways:
1. When p is a factor of the constant term, r, then:
• use the Division Property of Equality when p is a whole number or decimal.
• use the Multiplication Property of Equality when p is a fraction.
2. Regardless if p is or is not a factor of the constant term, r, you can use the Distributive Property.
3 -3 11
5 27 -53
101 8 238
-14 41
− 2
or 20 1
− 2
- 27
− 6
or - 4 1
− 2
Program: Pre-Algebra
Vendor: Aptara
Component: ANC_C08_L4
Grade: AMPDF Pages
Math Accelerated • Chapter 8 Equations and Inequalities
016_020_AM_ANC_C08_L4_664489.indd Page 16 25/07/12 2:43 AM s-019016_020_AM_ANC_C08_L4_664489.indd Page 16 25/07/12 2:43 AM s-019 /Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES.../Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES...
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NAME ___________________________________________________ DATE _____________________ PERIOD __________
Lesson 5 ReteachSolving Equations with Variables on Each Side
Example Solve 12x - 3 = 4x + 13. 12x - 3 = 4x + 13 Write the equation.
12x - 4x - 3 = 4x - 4x + 13 Subtraction Property of Equality
8x - 3 = 13 Simplify.
8x - 3 + 3 = 13 + 3 Addition Property of Equality
8x = 16 Simplify.
8x − 8 = 16 − 8 Division Property of Equality
x = 2 Simplify.
To check your solution, replace x with 2 in the original equation.
Check 12x - 3 = 4x + 13 Write the equation.
12(2) - 3 � 4(2) + 13 Replace x with 2.
24 - 3 � 8 + 13 Simplify.
21 = 21 � The statement is true.
Exercises Solve each equation. Check your solutions.
1. 2x + 1 = x + 11 2. a + 2 = 5 + 4a 3. 7y + 25 = 2y
4. n + 11 = 2n 5. 7 - 1 − 2 c = 1 − 4 c - 7 6. 4 - 3b = 6b - 5
7. 9d - 9 = 3d - 1.8 8. f - 4 = 6f + 26 9. -2s + 3 = 5s + 24
10. 2 − 3 a - 3 = 1 − 3 a + 6 11. 8n - 12 = -12n + 8 12. 7y + 8 = -2y - 64
13. 1 + 3x = 7x - 9 14. 6a - 3 = 4 + 7a 15. 3b - 1 = 14 + 2b
To solve equations with variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variable on one side. Then solve the equation.
Program: Pre-Algebra
Vendor: Aptara
Component: CRM_C08_L5
Grade: AMPDF Pages
Math Accelerated • Chapter 8 Equations and Inequalities
021_025_AM_ANC_C08_L5_664489.indd Page 21 25/07/12 2:43 AM s-019021_025_AM_ANC_C08_L5_664489.indd Page 21 25/07/12 2:43 AM s-019 /Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES.../Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES...
Co
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© T
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McG
raw
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l C
om
pa
nie
s, I
nc.
Pe
rmis
sio
n i
s g
ran
ted
to
re
pro
du
ce f
or
cla
ssro
om
use
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NAME ___________________________________________________ DATE _____________________ PERIOD __________
Lesson 5 ReteachSolving Equations with Variables on Each Side
Example Solve 12x - 3 = 4x + 13. 12x - 3 = 4x + 13 Write the equation.
12x - 4x - 3 = 4x - 4x + 13 Subtraction Property of Equality
8x - 3 = 13 Simplify.
8x - 3 + 3 = 13 + 3 Addition Property of Equality
8x = 16 Simplify.
8x − 8 = 16 − 8 Division Property of Equality
x = 2 Simplify.
To check your solution, replace x with 2 in the original equation.
Check 12x - 3 = 4x + 13 Write the equation.
12(2) - 3 � 4(2) + 13 Replace x with 2.
24 - 3 � 8 + 13 Simplify.
21 = 21 � The statement is true.
Exercises Solve each equation. Check your solutions.
1. 2x + 1 = x + 11 2. a + 2 = 5 + 4a 3. 7y + 25 = 2y
4. n + 11 = 2n 5. 7 - 1 − 2 c = 1 − 4 c - 7 6. 4 - 3b = 6b - 5
7. 9d - 9 = 3d - 1.8 8. f - 4 = 6f + 26 9. -2s + 3 = 5s + 24
10. 2 − 3 a - 3 = 1 − 3 a + 6 11. 8n - 12 = -12n + 8 12. 7y + 8 = -2y - 64
13. 1 + 3x = 7x - 9 14. 6a - 3 = 4 + 7a 15. 3b - 1 = 14 + 2b
To solve equations with variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variable on one side. Then solve the equation.
10 -1 -5
11 56
− 3
or 18 2
− 3
1
1.2 -6 -3
27 1 -8
2.5 -7 15
Program: Pre-Algebra
Vendor: Aptara
Component: CRM_C08_L5
Grade: AMPDF Pages
Math Accelerated • Chapter 8 Equations and Inequalities
021_025_AM_ANC_C08_L5_664489.indd Page 21 25/07/12 2:43 AM s-019021_025_AM_ANC_C08_L5_664489.indd Page 21 25/07/12 2:43 AM s-019 /Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES.../Volumes/104/GO01101_del/Accelerated_Maths_2014/PRE_ALGEBRA/ANCILLARIES...
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