# One-step equations

It is valid:$\forall a, b, c$

• if $a<b$, then $\forall c\in \mathbb{R}$:

$a+c<b+c$                                                   (1)

• if $a<b$, then $\forall c\in \mathbb{R}$:

$a \cdot c<b \cdot c$                                 (2)

•  if $a<b$ and $b<c$

$a<c$                                                            (3)

One-step equations is equations in form $ax+b=0$ and that can be solved in a single step.  We must find the value of the unknown variable (named $x$ in our case).

To find out the value of the unknown number in the example above, we need to get the equation in form of

$\ x = \frac{b}{a}, \forall a,b \in \mathbb{R}$.

Now, we will subtracting the number $2$ from both sides of t0he equality. It should look like this:

We use properties (1).

$x+2-2=5-2$

$x=3$

The value of our variable is number $3$.

Here is another example of a one step equation, but this one includes subtraction:

$x-5=1$

Now, we will do the same operations like in previous examine:

We use properties (1).

$x-5+5=1+5$

$x=6$

The result is $\ x = 6$.

The one-step equations can also contain multiplication or division. A one-step equation with multiplication can be solved by dividing both sides of the equation with the coefficient, which is the number that is multiplied by $x$

$6x=18$.

This example has been solved by dividing both sides of the equality with number $6$. We use properties (2).

$6x:6=18:6$

$x=3$

The result is $\ x = 3$.

A one-step equation that includes division can be solved in similar way. We just need to multiply both sides of the equality with the number that divides $x$.

$\frac{x}{4}=5$

In the example above, we need to multiply both sides by number $4$. We use properties (2).

$\frac{x}{4}\cdot 4=5 \cdot 4$

$x=20$

When we solve the equation, we see that the value of the variable is $20$.

So, this is basically it for the one-step equations. If you want, you can follow the link to the other lessons, such as the one on two-step equations.