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 obtain the following:

$x-1 + 1 = 5 + 1$

That is:

$X = 6$

This is the solution to our equation. We can always check if we are correct by inserting our answer into the original equation. Let's place$X=6$ into the equation

$X-1 = 5$

and we obtain the following

$6-1 = 5$

$5=5$

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

$Z + 7 = 15$

Upon observation we can see that the variable in this equation 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 the following:

$Z + 7 -7 = 15 – 7$

$Z = 8$

This is the solution to the equation. It's always a good idea to check if we have found the correct value of the unknown by placing our answer into the original equation.

Let's remember what the original equation was:

$Z + 7 = 15$

let's put

$Z = 8$

and we should obtain:

$8 + 7 = 15$

$15=15$

This is indeed a true statement, i.e., the answer is correct.

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

Determine the value of the unknown in the following equation and check whether it is correct.

$2X = 8$

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

$2X/2= 8/2$

and we should obtain :

$X = 4$

It is a good idea to place the solution into the original equation to check if our solution is correct:

$2\times 4 = 8$

$8 = 8$

This is indeed a true statement, i.e., the answer is correct.

Determine the value of the unknown in the following equation and verify that it is correct.

$-3Y = 18$

In order 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 a good idea to insert it back into the original equation. Try it!

Determine the value of the unknown in the following equation and verify that it is correct.

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

Here we have a fraction in the equation. Our goal is to remove it and to isolate the $X$. We multiply both members of the equation by. $3$

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

We obtain the following:

$x=15$

To verify this we will insert the obtained result into the original equation:

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

$5=5$

This is indeed a true statement, i.e., the answer is correct.

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

$2x + 3 = 5$

This exercise requires both subtraction and division 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 the following:

$2x/2 = 2/2$

$X = 1$

Let's insert the obtained result into the original equation to check if we have done it correctly:

$2\times 1 + 3 = 5$

$5 = 5$

This is indeed a true statement, i.e., the answer is correct.

Determine the value of the unknown in the following equation and verify that it is correct.

$​​​​​​​X-6=0$

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

After simplifying the expression we obtain the solution to the equation $X=6$ Due to the fact that if we insert $6$ instead of the $X$ we will obtain the result $0$ on both sides of the equation resulting in two equivalent members.

Determine the value of the unknown in the following equation and verify that it is correct.

$2X-6=0$

This exercise is comprised of an addition operation $6$ in both members of the equation, as follows:

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

$2X=6$

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

$2X/2=6/2$

$X=3$

The solution of the equation is $X=3$ due to the fact that if we insert $3$ in the place of the $X$ we should obtain the result $0$ on both sides of the equation, resulting in two equivalent members.

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

$3X-5=16$

This exercise requires us to add $5$ to both members of the equation, so we have the following:

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

$3X=21$

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

$3X/3=21/3$

$X=7$

The solution of the equation is $X=7$ due to the fact that if we insert $7$ in the place of $X$ we will obtain the result $16$ on both sides of the equation, resulting in two equivalent members.

Isolating the variable with mathematical operations.

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

Substituting the value found in the original equation and verifying that the statement of equality is satisfied.

It is the unknown value of the equation.

Isolating the variable with mathematical operations.

It is a mathematical statement of 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.