Digits, Grade 8, Volume 1, Homework Helper

Topic 6: Linear Equations in One Variable

6-1: Solving Two-Step Equations

Key Concept

You can think of solving an equation as transforming the equation into a series of simpler equivalent equations. Use the properties of equality to isolate the variable on one side of the equation.

A two-step equation involves two operations. To solve a two-step equation, it is usually easier to perform the order of operations in reverse. So undo addition or subtraction, and then undo multiplication of division.

Solve x over 4 , plus 12 equals 32 .

table with 4 rows and 3 columns , row1 column 1 , cap subtrehct . 1 2 . fromeehchside . . , column 2 x over 4 , plus 12 minus 12 , column 3 equals 32 minus 12 , row2 column 1 , cap simplify , . , column 2 x over 4 , column 3 equals 20 , row3 column 1 , cap multiplyeehchsideby . 4 . . , column 2 4 . open , x over 4 , close , column 3 equals 4 open 20 close , row4 column 1 , cap simplify , . , column 2 x , column 3 equals 80 , end table

Check

table with 3 rows and 3 columns , column 2 x over 4 , plus 12 , column 3 equals 32 , row2 column 1 , cap substitute . 8 0 , for . bold italic x . , column 2 80 over 4 , plus 12 , column 3 modified modified question mark with under bar below with under bar below , 32 , row3 column 1 , cap simplify , . , column 2 32 , column 3 equals 32 u 2 , end table

32 = 32 is a true statement, so when x over 4 , plus 12 equals 32 , x equals 80.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties