Download Two-Step Equations KEY

Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations KEY
The goal of solving an equation is to isolate the variable (get the variable by itself). This is done
by performing inverse operations. One-step equations are solved using addition/subtraction
properties or multiplication/division properties to isolate the variable. Remember, what you do to
one side of an equation, you must do exactly the same to the other side.
Two-Step Equations
Two-step equations combine the use of addition/subtraction and multiplication/division properties
to isolate the variable.
•
Use the addition/subtraction properties first to move the numeric value or
constant. The value on the same side of the equation and farthest away from the variable.
•
Then, use multiplication/division properties to isolate the variable.
Sample Problems
I.
Solve as indicated.
1. 2x + 7 = 5
Concrete Model Solution
Algebraic Solution
Graphic Solution,
Table
Solution
Check
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05/16/12
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y1 = 2x + 7
y2 = 5
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations KEY
2. 5x – 7 = –2
Concrete Model Solution
Algebraic Solution
Graphic Solution,
Table
Solution
Check
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©2012, TESCCC
05/16/12
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y1 = 5x – 7
y2 = -2
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations KEY
3.
1
5
x+3=4
Algebraic Solution
1
5
Graphic Solution,
Table
y1 = (1/5)x + 3
y2 = 4
x+3=4
Solution
Check
1
5
(5) + 3 = 4
1+3=4
4=4
1
5
x+3–3=4–3
1
5
x=1
1
5
( x) ● 5 = 1 ● 5
x=5
4. 8 – 3x = 14
Algebraic Solution
©2012, TESCCC
Graphic Solution,
Table
05/16/12
Solution
Check
page 5 of 11
8 – 3x = 14
8 – 3x – 8 = 14 – 8
-3x = 6
-3 -3
x = -2
y1 = 8 – 3x
y2 = 14
8 – 3(-2) = 14
8 + 6 = 14
14 = 14
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations KEY
II. Formulate an equation for the word problems. Solve the equation algebraically. Write a
statement to justify the solution.
5. Twice a number increased by four is fourteen. What is the number?
2x + 4 = 14
x=5
Two times five plus four does equal fourteen.
6. Five less than six times a number is seven. What is the number?
6x – 5 = 7
x=2
Six times two subtract five does equal seven.
7. At the local HUB’s grocery store, the cost of a carton of tamales, c, depends on the
number of tamales, t. The cost of the carton is $0.25 and each tamale is $0.50.
a. What equation could be used to represent this situation? c = 0.5t + 0.25
b. If a carton contained one dozen tamales, what would be the cost?
c = 0.5(12) + 0.25  c = 6.25
c. If the cost of a carton of tamales is $15.25, how many tamales are in the carton?
15.25 = 0.5x + 0.25  x = 30 tamales
III. Use the given information to solve for the indicated variable.
8. If (x, -2.8) is a solution to the equation 2x + 4y = 4.5, what is the value of x?
2x + 4(-2.8) = 4.5
2x – 11.2 = 4.5
2x = 15.7
x = 7.85
3
9. If (
3
3
8
, y) is a solution to the equation 8x = 3y – 7, what is the value of y?
3
8
8(
) = 3y – 7
27 = 3y – 7
34 = 3y
1
11
3
y=
©2012, TESCCC
05/16/12
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Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations KEY
Practice Problems
Solve as indicated.
1. 3x – 3 = 12
Concrete Model Solution
Algebraic Solution
Graphic Solution, Table
Solution Check
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©2012, TESCCC
05/16/12
page 9 of 11
y1 = 3x – 3
y2 = 12
2.
1
x +2 =1
3
Algebraic Solution
1
3
1
3
Graphic Solution, Table
y1 = (1/3)x + 2
y2 = 1
x+2=1
Solution Check
1
3
(-3) + 2 = 1
-1 + 2 = 1
1=1
x+2–2=1–2
1
3
x = -1
1
3
( x) ● 3 = -1 ● 3
x = -3
Two-Step Equations KEY
Formulate an equation for the word problems. Solve the equation algebraically. Write a
statement to justify the solution.
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
3. The product of three times a number increased by seven is seventeen. What is the
number?
3x + 7 = 17
3x = 10
1
3
x=3
1
3
Three times 3 equals ten. Seven added to ten equals 17.
4. Eleven decreased by twice a number is fifteen. What is the number?
11 – 2x = 15
x = -2
Eleven decreased by 2(-2) or -4, means to add four, so this does equal 15.
5. Surf City charges a base fee of $10 and $25 per hour to rent a surf board.
a) What equation could be used to represent the situation?
c = 25h + 10
b) If Toni rented a surf board for 5 hours, how much would she have to pay?
c = 25(5)+ 10  c = $135
c) Steven paid $185 for renting a surf board from Surf City. For how many hours
did Steven rent the surf board?
185 = 25h + 10  h = 7 hours
6. If (x, -4) is a solution to the equation 5x – 4y = 10, what is the value of x?
5x – 4(-4) = 10
5x + 16 = 10
5x = -6
6
1
− or − 1
5
5
x=
7. If (7, y) is a solution to the equation 2x + 3y = 44, what is the value of x?
2(7) + 3y = 44
14 + 3y = 44
3y = 30
y = 10
©2012, TESCCC
05/16/12
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