# What is the unknown of a mathematical equation?

๐Practice equation (+ what is the unknown)

But before explaining what unknowns are, it is important that we review the concept of what a mathematical equation is:

• An equation is an algebraic expression that includes numbers (fixed values), and also letters with unknown value (unknowns). Our goal is to arrive at a solution to the equation, that is, to find the missing value (the unknown), so that both sides of the equation are equal.

## What is an unknown?

In general, we express the unknowns with the letters $X$, $Y$ or Greek letters such as alpha and beta. Most of the time we will be asked to find the unknown value to be determined by solving an equation.

## Test yourself on equation (+ what is the unknown)!

$$5x=1$$

What is the value of x?

For example, in the equation $X+5=8$

In this exercise $X$ is the unknown to be found, and for this we will have to clear it. In this simple case all we have to do is subtract $5$ from both sides, and we will arrive at the answer.

$X+5=8$

$X+5-5=8-5$

$X=3$

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## Exercises with unknowns in equations

### Exercise 1

$14x+3=17$

Solution

We subtract $3$ from both sides of the equation, that is:

$14x+3-3=17-3$

$14x=14$

We divide by $14$ both sides of the equation:

$14x/14=14/14$

$x=1$

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### Exercise 2

Find the value of x in the following equation:

$2x+7-5x-12=-8x+3$

Solution

We pass the numerical values to the right and the coefficients that are multiplying to $X$ to the left.

$2x-5x+8x=+3-7+12$

Reduce and add as much as possible.

$5x=8$

We divide by $5$ both sides of the equation:

$x=\frac{8}{5}$

$x=\frac{8}{5}$

### Exercise 3

Find the value of $X$ in the following equation:

$5x=0$

Solution

We ask which number multiplied by $5$ is equal to $0$ and the answer is $0$

$5\cdot0=0$

$x=0$

Do you know what the answer is?

### Exercise 4

Find the value of $X$ in the following equation:

$5x=1$

Solution

We divide by $5$ both sides of the equation to find out how much is the value of $X$

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

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

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

### Exercise 5

Find the values of the variables so that the following equation is well defined:

$\frac{25a+4b}{7y+4\cdot3+2}=9b$

Solution:

We must calculate for which values of $Y$ the denominator of the expression on the left-hand side of the equation is equal to zero, i.e.:

$7y+4\cdot3+2= 0$

$7y+12+2=0$

$7y+14=0$

We subtract $14$ on both sides of the equation and we obtain:

$7y=-14$

Divide by $-7$ on both sides of the equation:

$y=-2$

If y equals minus $2$, then the denominator equals $0$ and the equation is not well defined:

$y\operatorname{\ne}-2$

$y\operatorname{\ne}-2$

## Questions on the subject

### What are the elements of an equation?

The variable and the fixed values or numbers.

### What is an unknown in an equation?

It is the unknown value to be found.

Do you think you will be able to solve it?

Variable

### How do you solve an equation with one unknown?

Clearing the unknown with the mathematical operations that are addition, subtraction, multiplication and division.

### How to clear a factor that is multiplying the unknown?

Dividing by the factor that is multiplying the unknown.

Do you know what the answer is?

## examples with solutions for equation (+ what is the unknown)

### Exercise #1

$5x=1$

What is the value of x?

### Video Solution

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

### Exercise #2

$5x=0$

### Video Solution

$x=0$

### Exercise #3

$14x+3=17$

### Video Solution

$x=1$

### Exercise #4

$2x+7-5x-12=-8x+3$

### Video Solution

$x=\frac{8}{5}$