Algebra Tutorials!

 Sunday 19th of May

 Home Calculations with Negative Numbers Solving Linear Equations Systems of Linear Equations Solving Linear Equations Graphically Algebra Expressions Evaluating Expressions and Solving Equations Fraction rules Factoring Quadratic Trinomials Multiplying and Dividing Fractions Dividing Decimals by Whole Numbers Adding and Subtracting Radicals Subtracting Fractions Factoring Polynomials by Grouping 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 Solving Quadratic Equations Simplifying Complex Fractions Algebra Common Logs Operations on Signed Numbers Multiplying Fractions in General Dividing Polynomials Polynomials 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 Straight Lines 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 Horizontal and Vertical Lines
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# 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 = 2Â·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.

 Copyrights © 2005-2024