Answer

Verified

405.6k+ 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.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

State the laws of reflection of light

State and prove Bernoullis theorem class 11 physics CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE