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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