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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
Lesson 12: Solving Equations
Isolate the variable so that it has a coefficient of 1.
Solve an Equation
Addition Property
of Equality
For any numbers a, b, c, if a = b, then
a+c=b+c
x – 7 = 21
Subtraction Property
of Equality
For any numbers a, b, c, if a = b, then
a-c=b-c
x + 7 = 21
Multiplication Property
of Equality
Division Property
of Equality
For any numbers a, b, c, if a = b, then
ac = bc.
For any numbers a, b, c, with c  0, if a = b, then
a=b
c c
x = 21
7
7x = 21
Solve each equation.
a. 6m + 7 = 19
b. 4 – 3x = 5
Lesson 12:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
c. 2x + 7 = 13
3 3 3
d. x – 1 = 5
4 3 12
Solving Equations
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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
e. Solve for 𝑟:
3
2𝑟
=
1
f. Solve for 𝑠: −4(3s − 1) = 12 − 9𝑠 + 5𝑠
4
g. Solve for 𝑦: 4𝑦 − 3 = 5𝑦 − 8
Consider the equation 3𝑥 + 4 = 8𝑥 – 16. Solve for 𝑥 using the given starting point.
Group 1
Subtract 3𝑥 from both sides
Group 2
Subtract 4 from both sides
Lesson 12:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Group 3
Subtract 8𝑥 from both sides
Group 4
Add 16 to both sides
Solving Equations
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NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 12
M1
ALGEBRA I
Consider the equation 𝒙𝟐 + 𝟏 = 𝟕 − 𝒙.
a. Verify that this has the solution set {2, −3}.
b.
Let’s add four to both sides of the equation
The new equation is ____________________________________.
Verify 2 and -3 are still solutions.
c.
Let’s now add 𝑥 to both sides of the equation
The new equation is ______________________________________________.
Are 2 and -3 still solutions?
d.
Let’s now subtract 𝑥 2 from both sides of the equation
The new equation is ______________________________________________.
Are 2 and -3 still solutions?
Lesson 12:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Solving Equations
5/5/17
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Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
ALGEBRA I
Problem Set 12A
Solve the following equations, distribute first to remove parentheses, check your solutions. Show work!!!
1. 2(6𝑏 + 8) = 4 + 6𝑏
ck.
3. − 16 − 6𝑣 = −2(8𝑣 − 7)
ck.
5. − 7 − 6𝑎 + 5𝑎 = 3𝑎 − 5𝑎
ck.
Lesson 12:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
2. 7 – 8𝑥 = 7( 1 + 7𝑥)
4. 39 − 8𝑛 = −8(3 + 4𝑛) + 3𝑛
6. 7 – 2𝑥 = 1 – 5𝑥 + 2𝑥
ck.
ck.
ck
Solving Equations
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M1
Lesson 12
NYS COMMON CORE MATHEMATICS CURRICULUM
ALGEBRA I
7. 4(𝑥 − 2) = 8(𝑥 − 3) − 12
8. − 5(2𝑟 − 0.3) + 0.5(4𝑟 + 3) = −64
ck.
ck.
9. Consider the equation -11 – 2p = 11p + 15. Solve for p using the given starting point.
Group 1
Add 2𝑝 to both sides
Group 2
Subtract 15 from both sides
Group 3
Subtract 11p from both sides
Group 4
Add 11 to both sides
10. Which of the following equations have the same solution set? Match equations below to each other. Give reasons
for your answers that do not depend on solving the equations.
I. 𝑥 – 5 = 3𝑥 + 7
II. 3𝑥 – 6 = 7𝑥 + 8
III. 15𝑥 – 9 = 6𝑥 + 24
IV. 6𝑥 – 16 = 14𝑥 + 12
V. 9𝑥 + 21 = 3𝑥 – 15
VI. −0.05 +
Lesson 12:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
𝑥
100
3𝑥
= 100
+ 0.07
Solving Equations
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