Systems of Equations
Adding and Subtracting Rational Expressions with Different Denominators
Graphing Linear Equations
Raising an Exponential Expression to a Power
Horizontal Line Test
Quadratic Equations
Mixed Numbers and Improper Fractions
Solving Quadratic Equations by Completing the Square
Solving Exponential Equations
Adding and Subtracting Polynomials
Factorizing simple expressions
Identifying Prime and Composite Numbers
Solving Linear Systems of Equations by Graphing
Complex Conjugates
Graphing Compound Inequalities
Simplified Form of a Square Root
Solving Quadratic Equations Using the Square Root Property
Multiplication Property of Radicals
Determining if a Function has an Inverse
Scientific Notation
Degree of a Polynomial
Factoring Polynomials by Grouping
Solving Linear Systems of Equations
Exponential Functions
Factoring Trinomials by Grouping
The Slope of a Line
Simplifying Complex Fractions That Contain Addition or Subtraction
Solving Absolute Value Equations
Solving Right Triangles
Solving Rational Inequalities with a Sign Graph
Domain and Range of a Function
Multiplying Polynomials
Slope of a Line
Multiplying Rational Expressions
Percent of Change
Equations Involving Fractions or Decimals
Simplifying Expressions Containing only Monomials
Solving Inequalities
Quadratic Equations with Imaginary Solutions
Reducing Fractions to Lowest Terms
Prime and Composite Numbers
Dividing with Exponents
Dividing Rational Expressions
Equivalent Fractions
Graphing Quadratic Functions
Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
Factoring Polynomials Completely
Using Slopes to Graph Lines
Fractions, Decimals and Percents
Solving Systems of Equations by Substitution
Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Adding and Subtracting Polynomials
The Rectangular Coordinate System
Polar Form of a Complex Number
Exponents and Order of Operations
Graphing Horizontal and Vertical Lines
Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
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Solving Equations

2-Step Equation

After studying this lesson, you will be able to:

  • Solve equations that require two steps.

Review of Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

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

3. 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

4. Check by substituting the solution into the original equation

Example 1

3x + 4 = 10 This equation will require 2 steps to solve it
3x + 4 -4 = 10 -4 First, we need to "undo" +4 so we subtract 4 from each side.

This gives us 3x = 6

Now, we need to "undo" 3 times x, so we divide each side by 3
x = 2 Now, we have the solution


substitute 2 for x in the original equation

3 (2) + 4 = 10

6 + 4 = 10

10 = 10 (notice that it also required 2 steps to check)


Example 2

-2x - 6 = 12 This equation will require 2 steps to solve it
-2x - 6 + 6 = 12 + 6 First, we need to "undo" -6 so we add 6 to each side

This gives us -2x = 18

Now, we need to "undo" -2 times x, so we divide each side by -2
x = -9 Now, we have the solution

Check: substitute -9 for x in the original equation

-2 (-9) -6 = 12

18 - 6 = 12

12 = 12


Example 3

This equation will require 2 steps to solve it
First, we need to "undo" +9 so we subtract 6 from each side

This gives us

Now, we need to "undo"

(which is x divided by 4), so we multiply each each side by 4.

x = -12 Now, we have the solution


substitute -12 for x in the original equation

-3 + 9 = 6

6 = 6

Example 4

In this equation, keep in mind that the expression 2-3x is being divided by 4

Since we're dividing an entire expression by another number, we need to deal with that first.

First, we need to "undo" the divided by 4 so we multiply each side by 4

This will eliminate the division and therefore simplify our equation. Notice that on the right-hand side, the fours cancel out each other

48 = 2-3x After multiplying both sides by 4 we get to this equation
48 -2 = 2-3x -2 Now, we need to "undo" the 2 (positive 2) so we subtract 2 from each side (Remember, we are trying to isolate the variable - get the x by itself, so we Need to get rid of the 2 first.) This will give us 46 = -3x
To "undo" the -3 times x, we divide each side by -3
This is the solution


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