Solution of an equation

In this article we will get to know the equations and learn simple ways to solve them.

Let's go back to the equation of the previous example:

$X-1 = 5$

We want to isolate $X$. To do this we will add $1$ to both members of the equation.

We will write it like this:

$X-1 = 5$

We will obtain:

$x-1 + 1 = 5 + 1$

That is:

$X = 6$

And, this is the solution to our equation. We can always check if we got it right by putting our answer in the original equation. Let's put $X=6$ into the equation

$X-1 = 5$

and we get

$6-1 = 5$

$5=5$

this is a true statement, $5$ really equals $5$, i.e., our solution is correct.

$Z + 7 = 15$

First let's see that this time the variable is $Z$. The variable can be denoted by any letter we want.

As we have explained before, we are interested in finding the value of the $Z$ that will give us the solution to the equation. Therefore, we will now try to isolate $Z$. We will do this by subtracting $7$ from the two members of the equation.

It looks like this:

$Z + 7 = 15$

We will obtain:

$Z + 7 -7 = 15 – 7$

$Z = 8$

This is the solution of the equation. Again, it is always convenient to check if we have found the correct value of the unknown by placing our answer in the original equation.

Let's remember what the original equation was:

$Z + 7 = 15$

let's put

$Z = 8$

and we will get:

$8 + 7 = 15$

$15=15$

This really is a true statement, i.e., the answer we received is correct.

So far we have solved equations by applying addition and subtraction operations to both sides of the equation. Now we will see other examples of equations that we will solve with multiplication and division operations:

Find the value of the unknown in the following equation and check that it is correct.

$2X = 8$

We want to isolate the $X$. We divide both members of the equation by $2$. We will write it like this:

$2X/2= 8/2$

and we will get :

$X = 4$

Also in this case it is convenient to place the solution in the original equation to see if we have done it right:

$2\times 4 = 8$

$8 = 8$

We obtained a correct result, that is, our solution is right.

Find the value of the unknown in the following equation and check that it is correct.

$-3Y = 18$

To isolate the variable Y we divide both members of the equation by $-3$

$-3Y/-3 = 18/-3$

$Y = -6$

To verify our result, it is always convenient to place it in the original equation. Try it!

Find the value of the unknown in the following equation and check that it is correct.

$\frac{1}{3}x=5$

Here we have a fraction in the equation. We want to get rid of it and isolate the $X$. We multiply both members of the equation by. $3$

$3\times\frac{1}{3}x=3\times5$

We will obtain:

$x=15$

To verify this we will place the result obtained in the original equation:

$\frac{1}{3}\times 15=5$

$5=5$

That is, the result obtained is correct.

Find the value of the unknown in the following equation and check that it is correct.

$2x + 3 = 5$

This exercise requires subtracting and dividing operations. First, we subtract $3$ from the two members of the equation:

$2x + 3 = 5$

$2x + 3 - 3 = 5 – 3$

$2x = 2$

Now we will divide the two members of the equation by. $2$ and we obtain:

$2x/2 = 2/2$

$X = 1$

Let's place the result obtained in the original equation to check if we have done it right:

$2\times 1 + 3 = 5$

$5 = 5$

That is, the result obtained is correct.

Find the value of the unknown in the following equation and check that it is correct.

$​​​​​​​X-6=0$

This exercise requires the operation of adding $6$ in both members of the equation, so we have:
$​​​​​​​X-6+6=0+6$

Simplifying we obtain that the solution of the equation is $X=6$ since if we put $6$ instead of the $X$ we will obtain the result $0$ on both sides of the equation, we will have two equivalent members.

Find the value of the unknown in the following equation and check that it is correct.

$2X-6=0$

This exercise requires the operation of adding $6$ in both members of the equation, so we have:

$2X-6+6=0+6$

$2X=6$

Now we divide by $2$ both sides of the equation :

$2X/2=6/2$

$X=3$

The solution of the equation is $X=3$ because if we put $3$ instead of the $X$ we will get the result $0$ on both sides of the equation, we will have two equivalent members.

Find the value of the unknown in the following equation and check that it is correct.

$3X-5=16$

This exercise requires the operation of adding $5$ in both members of the equation, so we have:

$3X-5+5=16+5$

$3X=21$

Now we divide by $3$ both sides of the equation:

$3X/3=21/3$

$X=7$

The solution of the equation is $X=7$ since if we put $7$ instead of the $X$ we will get the result $16$ on both sides of the equation, we will have two equivalent members.

Isolating the variable with mathematical operations.

Passing like terms to each side of the equality and performing mathematical operations.

Substituting the value found in the original equation and check that the equality is satisfied.

It is the unknown value of the equation.

Isolating the variable with mathematical operations.

It is a mathematical equality involving a variable raised to the first power and fixed values that are numbers.

If this article interested you, you may also be interested in the following articles:

• First-degree equations with an unknown variable
• What is the unknown of a mathematical equation?
• Equivalent Equations
• Transposition of terms
• Solving equations by multiplying or dividing both members by the same number
• Solving equations by simplifying equal elements
• Solving equations using the distributive property

In the Tutorela Math Blog you will find a wide variety of articles about mathematics.