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	Multiplication by 111
	Adding Fractions
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	Multiplication by 50
	Solving Linear Inequalities in One Variable
	Simplifying Cube Roots That Contain Integers
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	Simple Trinomials as Products of Binomials
	Writing Linear Equations in Slope-Intercept Form
	Solving Linear Equations
	Lines and Equations
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	Absolute Value Function
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	Complex Numbers
	Factoring the Difference of Two Squares
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	Adding and Subtracting Radicals
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	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
	Slopes
	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 Linear Equations

Example 1

Solve: 3(2x - 6) = -2(x + 4) - 50.

Solution

Step 1 Remove parentheses.

Distribute 3 and distribute -2.

Step 2 On each side of the equation, combine like terms.

Combine -8 and -50.

Step 3 Isolate the variable.

Add 18 to both sides.

Simplify.

Add 2x to both sides.

Simplify.

Divide both sides by 8.

3(2x - 6)

6x - 18

6x - 18 + 18

6x + 2x

= - 2(x + 4) - 50

= - 2x - 8 - 50

= - 2x - 58

= - 2x - 58 + 18

= - 2x - 40

= - 2x - 40 + 2x

= - 40

Simplify.

Step 4 Check the solution in the original equation.

We leave the check to you.

= -5

The solution is x = -5.

Note:

We can also solve 6x - 18 = - 2x - 58 by first adding 2x to both sides:

6x - 18 + 2x

8x - 18

8x - 18 + 18

= - 2x - 58 + 2x

= - 58

= - 58 + 18

= - 40

= -5

The solution of the previous example was a unique real number.