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One-step equations – The simplest type of equations

one-step equations

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.

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