Solve for $x$:
$x+12=3$
Solve for $x$:
$x+12=3$
$x+12\r{-12}=3\r{-12}$
Solve for $x$:
$x+12=3$
$x+12\r{-12}=3\r{-12}$
$x=3\r{-12}$
Solve for $x$:
$x+12=3$
$x+12\r{-12}=3\r{-12}$
$x=3\r{-12}$
$x=-9$
Solve for $n$:
$n+3m=5m-1$
Solve for $n$:
$n+3m=5m-1$
$n+3m\r{-3m}=5m-1\r{-3m}$
Solve for $n$:
$n+3m=5m-1$
$n+3m\r{-3m}=5m-1\r{-3m}$
$n=5m\r{-3m}-1$
Solve for $n$:
$n+3m=5m-1$
$n+3m\r{-3m}=5m-1\r{-3m}$
$n=5m\r{-3m}-1$
$n=2m-1$
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!
Solve for $x$:
$x-4y=5y$
Solve for $x$:
$x-4y=5y$
$x-4y\r{+4y}=5y\r{+4y}$
Solve for $x$:
$x-4y=5y$
$x-4y\r{+4y}=5y\r{+4y}$
$x=9y$
Solve for $n$:
$n+5x-4y=3+6x$
Solve for $n$:
$n+5x-4y=3+6x$
First, let's take care of $y$:
$n+5x-4y\r{+4y}=3+6x\r{+4y}$
Solve for $n$:
$n+5x-4y=3+6x$
First, let's take care of $y$:
$n+5x-4y\r{+4y}=3+6x\r{+4y}$
$n+5x=3+6x\r{+4y}$
Solve for $n$:
$n+5x-4y=3+6x$
$n+5x=3+6x+4y$
Now let's take care of $x$:
$n+5x\r{-5x}=3+6x+4y\r{-5x}$
Solve for $n$:
$n+5x-4y=3+6x$
$n+5x=3+6x+4y$
Now let's take care of $x$:
$n+5x\r{-5x}=3+6x+4y\r{-5x}$
$n=3+6x\r{-5x}+4y$
Solve for $n$:
$n+5x-4y=3+6x$
$n+5x=3+6x+4y$
Now let's take care of $x$:
$n+5x\r{-5x}=3+6x+4y\r{-5x}$
$n=3+6x\r{-5x}+4y$
$n=3+x+4y$
Solve for $n$:
$n+5x-4y=3+6x$
$n+5x=3+6x+4y$
$n=3+x+4y$
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!
Solve for $x$:
$12x=13$
Solve for $x$:
$12x=13$
$\frac{\r{12}x}{\r{12}}=\frac{13}{12}$
Solve for $x$:
$12x=13$
$\frac{\r{12}x}{\r{12}}=\frac{13}{12}$
$x=\frac{13}{12}$
Solve for $n$:
$4.2n-5.1=1.9$
Solve for $n$:
$4.2n-5.1=1.9$
First, take care of the subtraction:
$4.2n-5.1\r{+5.1}=1.9\r{+5.1}$
Solve for $n$:
$4.2n-5.1=1.9$
First, take care of the subtraction:
$4.2n-5.1\r{+5.1}=1.9\r{+5.1}$
$4.2n=7$
Solve for $n$:
$4.2n-5.1=1.9$
$4.2n=7$
$\frac{\r{4.2}n}{\r{4.2}}=\frac{7}{4.2}$
Solve for $n$:
$4.2n-5.1=1.9$
$4.2n=7$
$\frac{\r{4.2}n}{\r{4.2}}=\frac{7}{4.2}$
$n=\frac{7}{4.2}$
Remember BEDMAS: Brackets, Exponents, Division & Multiplication, Addition & Subtraction.
Since we're isolating a variable, we work backwards.
Solve for $y$:
$4y-5x+12=11x+20$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+20\r{-12}$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+\g{8}$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+8$
$4y=11x+8\r{+5x}$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+8$
$4y=\g{16}x+8$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+8$
$4y=16x+8$
$$\frac{\r{4}y}{\r{4}}=\frac{16x+8}{4}$$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+8$
$4y=16x+8$
$$y=\frac{16x}{4}+\frac{8}{4}$$
Solve for $y$:
$4y-5x+12=11x+20$
$4y-5x=11x+8$
$4y=16x+8$
$$y=4x+2$$