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Using If-Then Moves in Solving Equations

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Common Core For Grade 7

Examples, videos, and solutions to help Grade 7 students learn how to build an algebraic expression using the context of a word problem and use that expression to write an equation that can be used to solve the word problem.

New York State Common Core Math Grade 7, Module 3, Lesson 8

Download worksheets for Grade 7, Module 3, Lesson 8

Lesson 8 Student Outcomes

• Students understand and use the addition, subtraction, multiplication, division, and substitution properties of equality to solve word problems leading to equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers.
• Students understand that any equation with rational coefficients can be written as an equation with expressions that involve only integer coefficients by multiplying both sides by the least common multiple of all the rational number terms.

Lesson 8 Summary

• Algebraic Approach: To “solve an equation” algebraically means to use the properties of operations and If-then moves to simplify the equation into a form where the solution is easily recognizable. For the equations we are studying this year (called linear equations), that form is an equation that looks like, x = "a number," where the number is the solution.
• If-then moves: If is a solution to an equation, it will continue to be a solution to the new equation formed by adding or subtracting a number from both sides of the equation. It will also continue to be a solution when both sides of the equation are multiplied by or divided by a non-zero number. We use these If-then moves to make zeros and ones in ways that simplify the original equation.
• Useful First Step: If one is faced with the task of finding a solution to an equation, a useful first step is to collect like terms on each side of the equation.


Example 1
Julia, Keller, and Israel are volunteer firefighters. On Saturday the volunteer fire department held its annual coin drop fundraiser at a streetlight. After one hour, Keller had collected $42.50 more than Julia, and Israel had collected $15 less than Keller. Altogether, the three firefighters collected $125.95. How much did each person collect?
Find the solution using a tape diagram.
What were the operations we used to get our answer?
The amount of money Julia collected is j dollars. Write an expression to represent the amount of money Keller collected in dollars.
Using the expressions for Julia and Keller, write an expression to represent the amount of money Israel collected in dollars.
Using the expressions written above, write an equation in terms of j that can be used to find the amount each person collected.
Solve the equation written above to determine the amount of money each person collected and describe any if-then moves used.

Example 2
You are designing a rectangular pet pen for your new baby puppy. You have 30 feet of fence barrier. On a whim, you decide that you would like the length to be 6 1/3 feet longer than the width.
Draw and label a diagram to represent the pet pen. Write expressions to represent the width and length of the pet pen. Find the dimensions of the pet pen.

Example 3
Nancy’s morning routine involves getting dressed, eating breakfast, making her bed, and driving to work. Nancy spends 1/3 of the total time in the morning getting dressed, 10 minutes eating breakfast, 5 minutes making her bed, and the remaining time driving to work. If Nancy spent 35 1/2 minutes getting dressed, eating breakfast, and making her bed, how long was her drive to work?
Write and solve this problem using an equation. Identify the if-then moves used when solving the equation.

Example 4
The total number of participants who went on the 6th grade field trip to the Natural Science Museum consisted of all of the 6th grade students and 7 adult chaperones. 2/3 of the total participants rode a large bus and the rest rode a smaller bus. If 54 of them rode the large bus, how many students went on the field trip?

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