Download Two-Step Equations

Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations
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
©2012, TESCCC
Algebraic Solution
Graphic Solution,
Table
05/16/12
Solution
Check
page 1 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
©2012, TESCCC
05/16/12
page 2 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations
2. 5x – 7 = –2
Concrete Model
Solution
©2012, TESCCC
Algebraic Solution
Graphic Solution,
Table
05/16/12
Solution
Check
page 3 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
©2012, TESCCC
05/16/12
page 4 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations
3.
1
x+3= 4
5
Algebraic Solution
Graphic Solution,
Table
Solution
Check
Graphic Solution,
Table
Solution
Check
4. 8 – 3x = 14
Algebraic Solution
©2012, TESCCC
05/16/12
page 5 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
©2012, TESCCC
05/16/12
page 6 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations
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?
6. Five less than six times a number is seven. What is the number?
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?
b. If a carton contained one dozen tamales, what would be the cost?
c. If the cost of a carton of tamales is $15.25, how many tamales are in the carton?
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?
3
9. If (
3
8
©2012, TESCCC
, y) is a solution to the equation 8x = 3y – 7, what is the value of y?
05/16/12
page 7 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
©2012, TESCCC
05/16/12
page 8 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations
Practice Problems
Solve as indicated.
1. 3x – 3 = 12
Concrete Model Solution
2.
Algebraic Solution
Graphic Solution, Table
Solution Check
1
x +2=1
3
Algebraic Solution
©2012, TESCCC
Graphic Solution, Table
05/16/12
Solution Check
page 9 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
©2012, TESCCC
05/16/12
page 10 of 11
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Two-Step Equations
Formulate an equation for the word problems. Solve the equation algebraically. Write a
statement to justify the solution.
3. The product of three times a number increased by seven is seventeen. What is the
number?
4. Eleven decreased by twice a number is fifteen. What is the number?
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?
b) If Toni rented a surf board for 5 hours, how much would she have to pay?
c) Steven paid $185 for renting a surf board from Surf City. For how many hours
did Steven rent the surf board?
6. If (x, -4) is a solution to the equation 5x – 4y = 10, what is the value of x?
7. If (7, y) is a solution to the equation 2x + 3y = 44, what is the value of x?
©2012, TESCCC
05/16/12
page 11 of 11