# Understanding Equations

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Lesson Plans and Worksheets for Grade 7
Lesson Plans and Worksheets for all Grades

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.

### Lesson 7 Student Outcomes

• Students understand that an equation is a statement of equality between two expressions.
• Students 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.

### Lesson 7 Summary

•In many word problems, an equation is often formed by setting an expression equal to a number. To build the expression, it is often helpful to consider a few numerical calculations with just numbers first.
• To determine if a number is a solution to an equation, substitute the number into the equation for the variable (letter) and check to see if the resulting number sentence is true. If it is true, then the number is a solution to the equation.

Relevant Vocabulary

Variable (description): A variable is a symbol (such as a letter) that represents a number, i.e., it is a placeholder for a number.
Equation: An equation is a statement of equality between two expressions.
Number Sentence: A number sentence is a statement of equality between two numerical expressions.
Solution: A solution to an equation with one variable is a number that, when substituted for the variable in both expressions, makes the equation a true number sentence.

Classwork

Opening Exercise
Your parents are redecorating the dining room and want to place two rectangular wall sconce lights that are 25 inches wide along a 10 foot, 8 inch wall, so that the distance between the lights and the distances from each light to the nearest edge of the wall are all the same. Design the wall and determine the distance.
Let the distance between a light and the nearest edge of a wall be x ft. Write an expression in terms of x for the total length of the wall, and then use the expression and the length of the wall given in the problem to write an equation that can be used to find that distance.
Now write an equation where y stands for the number of inches: Let the distance between a light and the nearest edge of a wall be y in. Write an expression in terms y of for the total length of the wall, and then use the expression and the length of the wall (in inches) given in the problem to write an equation that can be used to find that distance (in inches).

Example 1
The ages of three sisters are consecutive integers. The sum of their ages is 45. Find their ages.
a. Use a tape diagram to find their ages.
b. If the youngest sister is x years old, describe the ages of the other two sisters in terms of x, write an expression for the sum of their ages in terms of x, and use that expression to write an equation that can be used to find their ages.
c. Determine if your answer from part (a) is a solution to the equation you wrote in part (b). Exercise
1. Sophia pays a \$19.99 membership fee for an online music store.
a. If she also buys two songs from a new album at a price of each \$0.99, what is the total cost?
b. If Sophia purchases n songs for each \$0.99, write an expression for the total cost.
c. Sophia’s friend has saved \$118 but isn’t sure how many songs she can afford if she buys the membership and some songs. Use the expression in part (b) to write an equation that can be used to determine how many songs Sophia’s friend can buy.
d. Using the equation written in part (c), can Sophia’s friend buy 101, 100, or 99 songs?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.