Example Equation

Solve for $x$:

$x+12=3$

Example Equation

Solve for $x$:

$x+12=3$

$x+12\r{-12}=3\r{-12}$

Example Equation

Solve for $x$:

$x+12=3$

$x+12\r{-12}=3\r{-12}$

$x=3\r{-12}$

Example Equation

Solve for $x$:

$x+12=3$

$x+12\r{-12}=3\r{-12}$

$x=3\r{-12}$

$x=-9$

Example 2

Solve for $n$:

$n+3m=5m-1$

Example 2

Solve for $n$:

$n+3m=5m-1$

$n+3m\r{-3m}=5m-1\r{-3m}$

Example 2

Solve for $n$:

$n+3m=5m-1$

$n+3m\r{-3m}=5m-1\r{-3m}$

$n=5m\r{-3m}-1$

Example 2

Solve for $n$:

$n+3m=5m-1$

$n+3m\r{-3m}=5m-1\r{-3m}$

$n=5m\r{-3m}-1$

$n=2m-1$

Equations with Subtractions

For equations with subtractions, simply do the opposite to clear them. For addition, we subtracted the number. For subtraction, we add the number!

Example:

$x-5=10$

$x-5\r{+5}=10\r{+5}$

$x=15$

Similarly, we can check our answer to make sure we got it right.

$x-5=10$

$\g{15}-5=10$

$10=10$

Both sides are equal, so we got it right!

Example

Solve for $x$:

$x-4y=5y$

Example

Solve for $x$:

$x-4y=5y$

$x-4y\r{+4y}=5y\r{+4y}$

Example

Solve for $x$:

$x-4y=5y$

$x-4y\r{+4y}=5y\r{+4y}$

$x=9y$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

First, let's take care of $y$:
$n+5x-4y\r{+4y}=3+6x\r{+4y}$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

First, let's take care of $y$:
$n+5x-4y\r{+4y}=3+6x\r{+4y}$
$n+5x=3+6x\r{+4y}$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

$n+5x=3+6x+4y$

Now let's take care of $x$:
$n+5x\r{-5x}=3+6x+4y\r{-5x}$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

$n+5x=3+6x+4y$

Now let's take care of $x$:
$n+5x\r{-5x}=3+6x+4y\r{-5x}$
$n=3+6x\r{-5x}+4y$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

$n+5x=3+6x+4y$

Now let's take care of $x$:
$n+5x\r{-5x}=3+6x+4y\r{-5x}$
$n=3+6x\r{-5x}+4y$
$n=3+x+4y$

Example 2

Solve for $n$:

$n+5x-4y=3+6x$

$n+5x=3+6x+4y$

$n=3+x+4y$

Equations with Multiplications

Just like subtraction is the opposite of addition, division is the opposite of multiplication! Simply divide to get rid of the multiplication.

Example:

$3x=6$

$\frac{\r{3}x}{\r{3}}=\frac{6}{3}$

$x=2$

Now let's check our answer to make sure we got it right:

$3x=6$

$3(\g{2})=6$

$6=6$

We got it right!

Example

Solve for $x$:

$12x=13$

Example

Solve for $x$:

$12x=13$

$\frac{\r{12}x}{\r{12}}=\frac{13}{12}$

Example

Solve for $x$:

$12x=13$

$\frac{\r{12}x}{\r{12}}=\frac{13}{12}$

$x=\frac{13}{12}$

Example 2

Solve for $n$:

$4.2n-5.1=1.9$

Example 2

Solve for $n$:

$4.2n-5.1=1.9$

First, take care of the subtraction:
$4.2n-5.1\r{+5.1}=1.9\r{+5.1}$

Example 2

Solve for $n$:

$4.2n-5.1=1.9$

First, take care of the subtraction:
$4.2n-5.1\r{+5.1}=1.9\r{+5.1}$
$4.2n=7$

Example 2

Solve for $n$:

$4.2n-5.1=1.9$

$4.2n=7$

$\frac{\r{4.2}n}{\r{4.2}}=\frac{7}{4.2}$

Example 2

Solve for $n$:

$4.2n-5.1=1.9$

$4.2n=7$

$\frac{\r{4.2}n}{\r{4.2}}=\frac{7}{4.2}$

$n=\frac{7}{4.2}$

How did we know to do the subtraction first?

Remember BEDMAS: Brackets, Exponents, Division & Multiplication, Addition & Subtraction.

Since we're isolating a variable, we work backwards.

Example

Solve for $y$:

$4y-5x+12=11x+20$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+20\r{-12}$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+\g{8}$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+8$

$4y=11x+8\r{+5x}$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+8$

$4y=\g{16}x+8$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+8$

$4y=16x+8$

$$\frac{\r{4}y}{\r{4}}=\frac{16x+8}{4}$$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+8$

$4y=16x+8$

$$y=\frac{16x}{4}+\frac{8}{4}$$

Example

Solve for $y$:

$4y-5x+12=11x+20$

$4y-5x=11x+8$

$4y=16x+8$

$$y=4x+2$$

Thank you!