Linear Equation

Solving Linear Equations

Linear Equation:

-A mathematical expression that has an equal sign and linear expressions

Variables

-A number that you don`t know, often represented by `x` or `y` but any letter will do!

Variable(s) in linear expressions

-Cannot have exponents (or powers)

for example: x squared or x^2

-Cannot multiply or divide each other

for example: `x` times `y` or xy, `x` divided by `y` or x/y

-Cannot be found under a root sign or square root (sqrt)

for example: √x or the `square root x `; sqrt (x)

Linear Expressions:

-A mathematical statement that performs functions of addition, subtraction, multiplication, and division

These are examples of linear expressions

x+4 , 2x+4 , 2x+4y

These are not linear expressions:

x^2 (no exponents on variables)

3xy+5 (can`t multiply two variables)

2x/6y (can`t divide two variables)

√x (no square root sign or variables)

Solve these linear equations by clicking and dragging 
a number to the "other" side of the equal sign. 
Remember that you are "isolating" the unknown "X" to solve the problem. 
(More examples are provided below.)

Isolate x in order to solve the equation. Click on parts of the equation on the left side and drag them to the right side.

3x-8=7

More examples:

Linear equation, solving example #1

Find x if: 2x+4=10

1. Isolate `x` to one side of the equation by subtracting 4 to both sides: 
2x+4-4=10-4

2x=6

2. Divide both sides by 2: 
2x/2=6/2

x=3

3. Check your work with the original equation:
2x+4=10

2(3) + 4=10

6+4=10

Linear equation, solving example #2

Find x if: 3x-4=-10

1. Isolate `x` to one side of the equation by adding 4 to both sides: 
3x-4+4=-10+4

3x=-6

2. Divide both sides by 3: 
3x/3=-6/3

 x=-2

3. Check your work with the original equation: 
3(-2)-4=-10

-6-4=-10

Linear equation, solving example #3:

Find x if: 4x-4y=8

(using more than one variables)

1. First step is to isolate `x` to one side of the equation by adding 4y to both sides: 
4x-4y+4y=8+4y

 4x=8+4y

2. Second step is to divide both sides by 4: 
4x/4 = (8+4y)/4

 x=2+y

3. Check your work with the original equation: 
4(2+y) - 4y=8

8+4y-4y=8

8=8

Linear equation, solving example #4:

Find x if x+3^2 =12

Note: since the square is on the number and not on the variable, the expression qualifies as a linear expression

1. First step is to square the number: 
x+3^2=12

x+9=12

2. Second step is to subtract both sides by 
9: x+9-9=12-9

 x=3

3. Check your work with the original equation:
3+3^2=12

12=12