Download Solve an Equation with Variables on Both

[Algebra 1 (X)]
3.5: Solving Equations with the Variable on Each Side Hawaii Content and Performance Standards III 


Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations. Benchmark MA.AI.10.1: Solve linear equations and inequalities in one variable using a variety of strategies. Benchmark MA.AI.10.3: Justify the steps used in simplifying expressions and solving equations and inequalities. Common Core State Standards for High School Mathematics 

A.REI.1: Understand solving equations as a process of reasoning and explain the reasoning. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3: Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Objectives:  To solve equations with the variable on each side.  To solve equations involving grouping symbols. Solving Equations in One Variable
Steps to Solving Multi‐Step Equations 1. Simplify the expressions on both sides of the equal sign (use the distributive property, combine like terms, etc). 2. Make sure the variable you want to solve is on one side of the equal sign. Use the Addition or Subtraction Property of Equality to move the variables to ONE SIDE of the equal sign. 3. Determine the order of operations occurring to the variable. 4. Undo each operation by using its inverse operation. Example 1: Solve an Equation with Variables on Both Sides Solve each equation. Then check your solution. a.) 2 10
8
1 b.) 8
5
7
2 Example 2: Solve an Equation with Grouping Symbols Solve each equation. Then check your solution. a.) 4
2
8
49
70 b.) 18
12
6 2
7 Example 3: No Solution or Infinitely Many Solutions Solve each equation. 5 5
a.) 2
7
3
b.) 4
20
20
400