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Solving Linear Equations
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Evaluating Expressions and Solving Equations
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Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Percents
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
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Algebra
Common Logs
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Multiplying Fractions in General
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Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
fractions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
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Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Quadratics
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Decimals
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
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Linear Equations

Equations that can be written in the form ax + b = 0 where a and b are real numbers, with a0, are linear equations. Examples oflinear equations include 5y + 9 = 16 and 8x = 4

The following properties are used to solve linear equations.

PROPERTIES OF EQUALITY

For all real numbers a, b, and c:

1. If a = b then a + c = b + c Addition property of equality (The same number may be addedto both sides of an equation.)

2. If a = b then ac = bc Multiplication property of equality (Both sides of an equation may be multiplied by the same number.)

Solving Linear Equations

EXAMPLE

(a) If x -2 = 3 then x = 2 + 3 = 5 Addition property of equality

(b) If x/2=3 then x = 2·3 = 6 Multiplication property of equality

The following example shows how these properties are used to solve lineare quations. Of course, the solutions should always be checked by substitution inthe original equation.

EXAMPLE

Solve 2x - 5 + 8 = 3x + 2(2-3x)

Solution

2x - 5 + 8 = 3x + 4-6x Distributive property

2x + 3 = -3x + 4 Combine like terms

5x + 3 = 4 Add 3x to both sides

5x = 1 Add -3 to both sides

Multiply both sides by .

Check by substituting in the original equation. The left side becomes 2(1/5)-5+8 and the right side becomes 3(1/5)+2(2-3(1/5)). Verify that both of these expressions simplify to 17/5.

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