# Linear Equations and Formulas

Definitions:

Solution: A number that makes an
equation true when it replaces the
variable in the equation .

Solution set : A set containing all the
solutions for a given equation.

Linear equation in one variable : An
equation with only one variable; the
variable is not raised to a power .

Identity: An equation in which every real
number (for which the equation is
defined) is a solution.

Contradiction: An equation that has no
solution.

If a=b, then a+c=b+c is true for all real numbers a, b, and c.
(If an equation is true and the same number is added to both sides, the equation is still
true.)

Multiplication Principle of Equality:
If a=b, then ac=bc is true for all real numbers a, b, and c, where c=0.
(If an equation is true and both sides are multiplied by the same number, the equation
is still true.)

## Pattern for solving linear equations in 1 variable:

1. Distribute to clear parentheses
2.Multiply to clear fractions and decimals
3. Combine like terms .

Now it is ready, so SOLVE it:
1. Get variable on only one side
2. Get constants on the other side
3. Eliminate the coefficient of the variable
using multiplication principle.

Now you've solved it, so CHECK it.
1. Substitute the possible solution for the variable
2. Simplify both sides
3. If the result is true, it is a solution
If the result is false, it is not a solution.

## Pattern for solving linear equations in 1 variable:

Now you've solved it, so CHECK it.
1. Substitute the possible solution for the variable
2. Simplify both sides
3. If the result is true, it is a solution
If the result is false, it is not a solution.

To isolate a particular variable in a formula:
1. Treat all other variables as constants.
2. Isolate the desired variable using the pattern for solving equations.

Just make up a digit to put in place of each of
the variables you are NOT solving for... use the
same steps to solve the formula that you would
use to solve the similar equation

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of August 20th you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!