Curriculum / Math / 8th Grade / Unit 2: Solving One-Variable Equations / Lesson 6
Math
Unit 2
8th Grade
Lesson 6 of 12
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Solve equations with variables on both sides of the equal sign.
The core standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
The foundational standards covered in this lesson
7.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
The equation $$2x+3=7$$ can be shown using a balance, like below, where each bag contains an unknown number of tiles, $$x$$.
Solving this equation can be shown using the picture by keeping the balance level. The solution below shows $$x=2$$.
a. Solve $$5x+1=2x+7$$ in two ways: symbolically, the way you usually do with equations, and also with pictures of a balance. Show how each step you take symbolically is shown in the pictures.
b. Solve the equation $$4x=x+1$$ using pictures and symbols. Discuss any issues that arise.
Solving Equations, accessed on Aug. 31, 2017, 1:47 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
The equation below is solved incorrectly three different ways.
For each solution, find and explain the error(s) that occurred. Then find the correct solution for $$y$$.
$${12-4y=7y+10}$$
$${22=3y}$$
$${7\frac{1}{3}=y}$$
$$12=11y+10$$
$$11y=-2$$
$$y=-\frac{2}{11}$$
$${4y=7y+22}$$
$${-3y=22}$$
$${y=-7\frac{1}{3}}$$
What value for $$x$$ would make the following equation true?
$$20-(3x-9)-2=-(-11x+1)$$
Grade 8 Mathematics > Module 4 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
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Three expressions are shown below.
Using the expressions in the chart, find the value of $$x$$ in each situation described.
a. A = C
b. A + B = C
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 5
Lesson 7
Topic A: Simplifying Expressions and Verifying Solutions
Write equivalent expressions using properties of operations and verify equivalence using substitution.
8.EE.C.7
Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.
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Topic B: Analyzing and Solving Equations in One Variable
Justify each step in solving a multi-step equation with variables on one side of the equation.
8.EE.C.7.A 8.EE.C.7.B
Write and solve multi-step equations to represent situations, with variables on one side of the equation.
8.EE.C.7.B
Model with equations using a three-act task.
Write and solve multi-step equations to represent situations, including variables on both sides of the equation.
Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.
8.EE.C.7.A
Solve and reason with equations with three types of solutions.
Use equations to model a business plan and determine the break-even point.
Topic C: Analyzing and Solving Inequalities in One Variable
Solve and graph inequalities with variables on one side of the inequality (optional).
A.REI.B.3
Solve and graph inequalities with variables on both sides of the inequality (optional).
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