# Solve for the value of x if $5\left( {8x + 3} \right) = 9\left( {4x + 7} \right)$.

Answer

Verified

324.3k+ views

Hint- Here, we are given with one equation in one variable (x) which can be easily solved by using the basic principles of algebra. Here, we will rearrange the given equation so that we can get the value for variable x.

Complete step-by-step answer:

The given equation is $

5\left( {8x + 3} \right) = 9\left( {4x + 7} \right) \\

\Rightarrow 40x + 15 = 36x + 63{\text{ }} \to {\text{(1)}} \\

$

Now, the given equation is reduced to equation (1) from which we can easily say that in this equation (1) there is only one variable x.

Shifting the term 36x (present on the RHS) towards LHS and the term 15 (present on the LHS) towards RHS in equation (1), we get

$

\Rightarrow 40x - 36x = 63 - 15 \\

\Rightarrow 4x = 48 \\

$

Now, by shifting 4 (which is getting multiplied on the LHS) to the RHS it will be divided by 48 in the above equation.

$

\Rightarrow 4x = 48 \\

\Rightarrow x = \dfrac{{48}}{4} = 12 \\

$

So, the required value of x which satisfies the given equation is 12.

Note- In this particular problem, we have used the concepts like when a term is shifted from the LHS to the RHS or from the RHS to the LHS of any equation, the sign of that term changes. Also, when a number which is multiplied on the LHS or the RHS is shifted to the RHS or the LHS of that equation respectively, that number comes in division.

Complete step-by-step answer:

The given equation is $

5\left( {8x + 3} \right) = 9\left( {4x + 7} \right) \\

\Rightarrow 40x + 15 = 36x + 63{\text{ }} \to {\text{(1)}} \\

$

Now, the given equation is reduced to equation (1) from which we can easily say that in this equation (1) there is only one variable x.

Shifting the term 36x (present on the RHS) towards LHS and the term 15 (present on the LHS) towards RHS in equation (1), we get

$

\Rightarrow 40x - 36x = 63 - 15 \\

\Rightarrow 4x = 48 \\

$

Now, by shifting 4 (which is getting multiplied on the LHS) to the RHS it will be divided by 48 in the above equation.

$

\Rightarrow 4x = 48 \\

\Rightarrow x = \dfrac{{48}}{4} = 12 \\

$

So, the required value of x which satisfies the given equation is 12.

Note- In this particular problem, we have used the concepts like when a term is shifted from the LHS to the RHS or from the RHS to the LHS of any equation, the sign of that term changes. Also, when a number which is multiplied on the LHS or the RHS is shifted to the RHS or the LHS of that equation respectively, that number comes in division.

Last updated date: 27th May 2023

â€¢

Total views: 324.3k

â€¢

Views today: 2.83k

Recently Updated Pages

Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?