Quick Hints for Equations

Solving Linear Equations

A Linear Equation is an equation that can be written in the form ax = b where a and b are constants and a does not equal 0.
There are four options you can use when solving a linear equation:

Solving an Equation with a Variable on One Side


2x - 4x = -5
  
-2x = -5
Combine like terms
x = 5/2
Divide by -2

Solving an Equation with a Variable on Both Sides


5n + 11 = 7n - 9
  
 11 = 2n - 9
Subtract 5n from each side
20 = 2n
Add 9 to each side
10 = n
Divide each sie by 2

Using the Distributive Property


2(x + 6) = -2(x - 4)
  
2x + 12 = -2x + 8
Distributive Property
4x + 12 = 8
Add 2x to each side
4x = -4
Subtract 12 from each side
x = -1
Divide each side by 4

Solving an Equation with Fractions


1/3x + 1/4 = x - 1/6
  
12(1/3x + 1/4) = 12(x - 1/6)
Multiply each side by the LCD, 12
4x + 3 = 12x - 2
Distributive Property
3 = 8x - 2
Subtract 4x from each side
5 = 8x
Add 2 to each side
5/8 = x
Divide each side by 8

Solving Literal Equations

A Literal Equation had more that on variable and is solved for a specific variable in terms of the other variables. A numeric answer is not available for this type of equation.


7x - 3y = 8  for y
  
-3y = -7x + 8
Subtract 7x from each side
y = 7/3x - 8/3
Divide each side by -3

Writing Equations of Lines

There are 3 forms for writing the equation of a line:


Slope-Intercept Form
In order to write an equation in slope-intercept form, you must have the slope (m) and the y-intercept (b).

Slope = 3/2        y-intercpet = -1


y = mx + b
  
y = 3/2x + b
Insert the slope (m)
y = 3/2x - 1
Insert the y-intercept (b)

 

Point Slope
In order to write an equation in Point Slope form, you must have the slope and a point.

Slope = -1/2      Through (2,3)


 
y-y1 = m(x-x1)
  
y-3 = m(x-3)
Insert Points
y-3 = (-1/2)(x-3)
Insert Slope

Standard Form
In order to write an equation in Standard form, you must have the slope and the y-interept.

Slope = 3/2       y-intercept = -1


 
 
y = mx + b
Start with Slope-Intercept Form
y = (2/3)x - 1
Insert Slope and y-intercept
2y = 3x - 1
Multpily times 2
3x - 2y = 1
>
Subtract 3x from each side and Multiply times -1

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