HOME
solving equations fractions 2
solving quadratic equations 4
equations 4
solving equations 9
linear equations 3
solving equations 6
solving equations 12
solving equations 8
linear equations 2
solving linear equations 2
solving linear equations 4
solving equations 13
solving quadratic equations 2
solving equations 10
solving equations 7
solving linear equations 3
quadratic equations 2
linear equations 4
solving equations 11
solving rational equations 2
equations 2
solving equations 4
solving systems linear equations 2
solving linear equations 5
solving equations 3
solving quadratic equations 3
solving quadratic equations 5
equations 3
solving equations 5
solving equations 2

Solving Linear Equations

Solving Linear Equations

Solve the following nonstandard linear equation for x and check your answer by substitution.

x - 3 = 4x -18  
x - 3 + 3 = 4x - 18 + 3 Add 3 to both sides
x = 4x -15 Collect like terms
x - 4x = 4x - 4x -15 Subtract 4x from both sides
-3x = -15 Collect like terms
Divide both sides by 3
x = 5  

 

CHECK: Substitute 5 for each x in the original equation

and the solution checks

 

*** MY RULE THAT MAKES IT EASIER TO SOLVE THESE EQUATIONS!! ***

YOU CAN MOVE A TERM FROM ONE SIDE TO THE OTHER AS LONG AS YOU CHANGE ITS SIGN !!!! THE OBJECT IS TO GET ALL OF THE x TERMS ON THE LEFT SIDE OF THE EQUATION AND ALL OF THE CONSTANT TERMS ON THE RIGHT SIDE OF THE EQUATION.

EXAMPLE: Solve 2x + 6 = 3x + 5

2x - 3x = +5 - 6

Note:

I left 2x on the left side -> sign stays same

I moved 3x from the right side to the left side -> its sign changed

I left +5 on the right side -> sign stays same

I moved +6 from the left side to the right side -> its sign changed

Now all the x terms are on the left and all the constant terms are on the right. So collect like terms and solve.

-x = -1 but you need to solve for x not -x!!

So multiply both sides of the equation through by -1. Thus

(-1)(-x) = (-1)(-1) x = 1 is your answer !!!

CHECK: Substitute 1 for each x in the original equation

2x + 6 = 3x + 5 Original equation

Substitute 1 for x

and thus your solution checks !!!

If an equation involves fractions, get rid of the fractions first by multiplying both sides of the equation through by their lowest common denominator - the smallest number that all the denominators will divide into evenly.

Solve: Multiply each term in the equation by 6 which is the LCD of 6 and 3

x + 2 = 6

x = 6 - 2

x = 4

CHECK: Original equation

Substitute 4 for x

1 = 1 so the solution checks !!!!!

If an equation involves decimals, get rid of the decimals first by multiplying both sides of the equation through by an appropriate power of 10 - that is, use 10, 100, 1000, etc

EXAMPLE: .3x + 1.5 = 8.4

If we multiply this equation by 10, it won't have any more decimals!

.3x + 1.5 = 8.4 Original equation
10(.3x + 1.5) = 10(8.4) Multiply both sides by 10
3x + 15 = 84  
3x = 84 - 15 Move terms to correct side
3x = 69 Collect terms
Divide both sides by 3
x = 23  

Check:.3x + 1.5 = 8.4 Original equation

Substitute 23 for x

8.4 = 8.4 and the solution checks !

ONE FRACTION is set equal to ANOTHER FRACTION

If one single fraction is set equal to another single fraction, then you can simply cross multiply! That is, multiply one numerator by the opposite denominator and set that equal to the other numerator multiplied by the other denominator. Then solve as a normal equation!

EXAMPLES:

Note: one fraction is set equal to another 14 7 fraction

7(x+4) = 2(14)

7x + 28 = 28

7x = 28 - 28

7x = 0

x = 0

Note: One fraction is set equal to another fraction

9(2x - 8) = 4(x + 3)

18x -72 = 4x + 12

18x - 4x = 72 + 12

14x = 84

x = 6

Buy  Algebrator now: 

Instant download and optional CD

Only $39.99

Click to Buy Now:



OR

Attention: We are currently running a special promotional offer for equation-solver.com Visitors -- if you order Algebrator by midnight of July 4th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35.00 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 minutes of live math tutoring from tutor.com!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebrator is:

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

Step 2 : Let Algebrator solve it:

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

Algebrator 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
  • operations with complex numbers (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...)

Buy  Algebrator now: 

Instant download and optional CD

Only $39.99

Click to Buy Now:



OR






















2009-07-04 03:26:48