MandysNotes

Linear Equations

Linear Equations (5)

4x - 2x - 5 = 4 + 6x + 3

Goal is to isolate x on one side to be able to solve.

2x - 5 = 7 + 6x

Combine like terms.

2x - 5 + 5 = 7 + 6x + 5

Add 5 to each side.

2x = 12 + 6x

Subtract 6x from each side.

-4x = 12

Then, divide both sides by -4

x = -3

CHECK your solution by plugging back into the original equation.


Disclaimer: I did not create nor do I own these videos. I have simply embedded them, courtesy of YouTube.  (But I do think this teacher does a fantastic job with his video tutorial series.)

Here is a list of steps to remember when solving Linear Equations in One Variable.

You may want to become familiar with these steps, each one on its own before putting them all together!

STEP 1: Clear fractions. Get rid of any fractions you see in the original equation by multiplying each side by the least common denominator.

STEP 2: Simplify each side. Use the distributive property to get rid of parentheses and/or combine like terms as necessary.

STEP 3: Isolate the variable terms (often "x") on one side. Use varying properties to get all terms with variables on one side of the equation, with all nubers on the other.

STEP 4: Isolate the variable. Use properties to get an equation with just the variable on one side.

STEP 5: CHECK your solution. Substitute your answer back into the ORIGINAL equation to make sure it is correct.

2(k - 5) + 3k = k + 6

Use the distributive property to simplify and combine like terms.

2k - 10 + 3k = k + 6

Combine like terms.

5k - 10 = k + 6

Then, add 10 to both sides.

5k = 16 + k

Then, subtract k from both sides.

4k = 16

Then, divide both sides by 4

k = 4

CHECK your solution by plugging back into the original equation.

 

Disclaimer: I did not create nor do I own these videos. I have simply embedded them, courtesy of YouTube.  (But I do think this teacher does a fantastic job with his video tutorial series.)

Sunday, 21 March 2010 17:55

Linear Equations in One Variable

By

As the name suggests, a linear equation in one variable implies that there is only ONE variable, and that the equation involves only real numbers. A linear equation in one variable can be written in this form: Ax + B = C where A does NOT equal zero.

A linear equation is also a first-degree equation, since the greatest power of any variable is 1.

Here are some examples of linear equations in one variable:

x + 2 = -1

x - 3 = 5

3k + 4 = 10

Equations and Expressions are closely related.

The primary difference between the two is an equals sign. An "equation" has a left side, a right side and an equals sign separating the sides. An "expression," by contrast, doesn't have any "sides" and is simply what the name suggests: An algebraic "expression." Though sometimes it is possible to combine like terms, we are generally not expected to "do" or "solve" anything regarding expressions.

For example:

3x - 7 = 2

This is an EQUATION, because it has a left side, a right side, and an = sign separating the two.

3x - 7

This is an EXPRESSION, because there are no "sides" and no = sign.

NOTRad