What is the unknown of a mathematical equation?

πŸ†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 X , Y 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.

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

einstein

\( 5x=1 \)

What is the value of x?

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

In this exercise X 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 5 from both sides, and we will arrive at the answer.

X+5=8 X+5=8

X+5βˆ’5=8βˆ’5 X+5-5=8-5

X=3 X=3

A - What is the unknown of a mathematical equation


Exercises with unknowns in equations

Exercise 1

14x+3=17 14x+3=17

Solution

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

14x+3βˆ’3=17βˆ’3 14x+3-3=17-3

14x=14 14x=14

We divide by 14 14 both sides of the equation:

14x/14=14/14 14x/14=14/14

Answer

x=1 x=1


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Exercise 2

Find the value of x in the following equation:

2x+7βˆ’5xβˆ’12=βˆ’8x+3 2x+7-5x-12=-8x+3

Solution

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

2xβˆ’5x+8x=+3βˆ’7+12 2x-5x+8x=+3-7+12

Reduce and add as much as possible.

5x=8 5x=8

We divide by 5 5 both sides of the equation:

x=85 x=\frac{8}{5}

Answer

x=85 x=\frac{8}{5}


Exercise 3

Find the value of X X in the following equation:

5x=0 5x=0

Solution

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

5β‹…0=0 5\cdot0=0

Answer

x=0 x=0


Do you know what the answer is?

Exercise 4

Find the value of X X in the following equation:

5x=1 5x=1

Solution

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

5x5=15 \frac{5x}{5}=\frac{1}{5}

x=15 x=\frac{1}{5}

Answer

x=15x=\frac{1}{5}


Exercise 5

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

25a+4b7y+4β‹…3+2=9b \frac{25a+4b}{7y+4\cdot3+2}=9b

Solution:

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

7y+4β‹…3+2=0 7y+4\cdot3+2= 0

7y+12+2=0 7y+12+2=0

7y+14=0 7y+14=0

We subtract 1414 on both sides of the equation and we obtain:

7y=βˆ’14 7y=-14

Divide by βˆ’7 -7 on both sides of the equation:

y=βˆ’2 y=-2

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

yβ‰ β‘βˆ’2 y\operatorname{\ne}-2

Answer

yβ‰ β‘βˆ’2 y\operatorname{\ne}-2


Check your understanding

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?

What is the unknown called in algebraic language?

Variable


How do you solve an equation with one unknown?

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


Test your knowledge

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 5x=1

What is the value of x?

Video Solution

Answer

x=15 x=\frac{1}{5}

Exercise #2

5x=0 5x=0

Video Solution

Answer

x=0 x=0

Exercise #3

14x+3=17 14x+3=17

Video Solution

Answer

x=1 x=1

Exercise #4

2x+7βˆ’5xβˆ’12=βˆ’8x+3 2x+7-5x-12=-8x+3

Video Solution

Answer

x=85 x=\frac{8}{5}

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