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.
