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Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
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Solving Two-Step Equations

Objective Learn to solve linear equations that involve more than one operation by using the Addition, Subtraction, Multiplication, and Division Properties of Equality.

This material is crucial in algebra. Thus, it is beneficial that you learn how to use these skills fluently.


Solving Two-Step Equations

Use the following examples to review the techniques for solving one-step equations.

Example 1

Solve x + 7 = 15.


x + 7 = 15  
x + 7 - 7 = 15 - 7 Subtract 7 from each side.
x = 8   The solution is 8.

In this example, we used subtraction to undo the addition of 7. Thus, we used the Subtraction Property of Equality.


Example 2

Solve 3x = 27.


3x = 27  
Divide each side by 3
x = 9 The solution is 9.

In this example, we used division to undo the multiplication of 3. Thus, we used the Division Property of Equality.

Sometimes, we encounter problems where there is both addition and multiplication in the equation. We must use both of these methods to solve these kinds of problems.


Example 3

Morgan bought a book for $10 and some CDs. The cost of each CD was $12. If Morgan spent a total of $46, how many CDs did she buy?


First, set up an equation. Let c represent the number of CDs Morgan bought. Since the cost of each CD is $12, the amount Morgan spent on CDs is given by 12c dollars. Morgan also spent $10 on a book. So, the total amount Morgan spent is

12c + 10 dollars.

We know that Morgan spent $46. So, we can write

12c + 10 = 46.

To solve this equation, we need to isolate c on the left side of the equation. This means we must undo the addition of 10 and the multiplication of 12. First, undo the addition of 10. Then undo the multiplication of 12.

12c + 10 = 46  
12c + 10 - 10 = 46 - 10 Subtract 10 from each side.
12c = 36  
Divide each side by 12.
c = 3  

So, Morgan bought 3 CDs.

The steps in solving two-step equations are:

(1) Undo any addition or subtraction. This leaves an equation with only multiplication or division.

(2) Undo any multiplication or division.

Try to write and solve various two-step equations by yourself. Be sure to include problems with negative coefficients and constants, and some fractions.

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