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TUTORIALS:

Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   
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Solving Equations with Variables on Each Side

After studying this lesson, you will be able to:

  • Solve equations with variables on each side of the equal sign.
  • Solve equations with parentheses and other grouping symbols.

Steps for Solving Equations with Variables on Each Side and with Parentheses

1. Remove parentheses by multiplying

2. Collect like terms on each side of the equal sign

3. Get the variables together on one side of the equation and get the numbers together on the other side of the equation.

4. Isolate the variable by "undoing" the operation (do this until the variable is by itself)

  1. "undo" addition and subtraction first
  2. next, "undo" multiplication and division

5. Check by substituting the solution into the original equation

 

Example 1

2x + 4 = 6x + 8 This equation doesn't have parentheses, but it does have a variable each side. It doesn't have like terms to collect on either side.
2x + 4 - 2x = 6x + 8 - 2x First, we need to get the variables together. It doesn't matter if we put them on the left side or the right side. Let's put them together on the right side this time. To do that, we move 2x to the other side by subtracting 2x from each side. Notice that we line up the like terms. (-2x is lined up with 6x so that it is easier to deal with.)
4 = 4x + 8 After collecting like terms (6x - 2x) we now have an equation where the variables are now together. Now, we work this as a 2-step equation.
4 - 8 = 4x + 8 - 8 We need to "undo" +8, so we subtract 8 from each side. This gives us -4 = 4x
Now, we need to "undo" 4 times x, so we divide each side by 4
-1 = x This is the solution

Check:

substitute -1 for each x in the original equation

2 (-1) + 4 = 6 (-1) +8 work out each side separately

-2 + 4 = -6 + 8 do the multiplying first

2 = 2

 

Example 2

6x - 3 = 2x + 13 This equation doesn't have parentheses, but it does have a variable each side. It doesn't have like terms to collect on either side.
6x - 3 - 2x = 2x + 13 - 2x First, we need to get the variables together. It doesn't matter if we put them on the left side or the right side. Let's put them together on the left side this time. To do that, we move 2x to the other side by subtracting 2x from each side. Notice that we line up the like terms. (-2x is lined up with 6x so that it is easier to deal with.)
4x -3 = 13 After collecting like terms (6x - 2x) we now have an equation where the variables are now together. Now, we work this as a 2-step equation.
4x -3 + 3 = 13 + 3 We need to "undo" -3, so we add 3 to each side.

This gives us 4x = 16

Now, we need to "undo" 4 times x, so we divide each side by 4
x = 4 This is the solution

Check:

substitute 4 for each x in the original equation

6 (4) - 3 = 2 (4) + 13 work out each side separately

24 - 3 = 8 + 13 do the multiplying first

21 = 21

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