Question

5
1
(2) The solution of the equation 3x –
2.
=
+ x is ...
2​

Answer 1

$3x - \frac{1}{2} = \frac{5}{x} + x \\ 3x - x = \frac{5}{2} + \frac{1}{2} \\ 2x = \frac{5 + 1}{2} \\ 2x = \frac{4}{2} \\ 2x = 2 \\ x = \frac{2}{2} \\ x = 1$

Answer 2

★ How to do :-

Here, we are given with an equation in which we have two variables and two constants and the equal sign. We are asked to find the value of the variable x. We can find the value of this variable easily by using other concepts. The concept used here is the transposition method. This method helps us to find the value of x. In this method, we shift the variables on LHS and all the constants on RHS. By this, we can simplify the constants and then, find the value of the variable. We can also verify our answer by verification method. So, let's solve!!

$\:$

➤ Solution :-

${\tt \leadsto 3x - \dfrac{1}{2} = \dfrac{5}{2} + x}$

Shift the variable on RHS to LHS and constant on LHS to RHS.

${\tt \leadsto 3x - x = \dfrac{5}{2} + \dfrac{1}{2}}$

Subtract the values on LHS and add the values on RHS.

${\tt \leadsto 2x = \dfrac{5 + 1}{2}}$

Add the numerators on RHS.

${\tt \leadsto 2x = \dfrac{6}{2}}$

Simplify the fraction on RHS.

${\tt \leadsto 2x = 3}$

Shift the number 2 from LHS to RHS.

${\tt \leadsto x = \dfrac{3}{2} = 1.5}$

$\:$

${\red{\underline{\boxed{\bf So, \: the \: value \: of \: x \: is \: \: \dfrac{3}{2} \: or \: 1.5}}}}$

━━━━━━━━━━━━━━━━━━━━━━

Verification :-

${\tt \leadsto 3x - \dfrac{1}{2} = \dfrac{5}{2} + x}$

Substitute the value of x.

${\tt \leadsto 3 \bigg( \dfrac{3}{2} \bigg) - \dfrac{1}{2} = \dfrac{5}{2} + \dfrac{3}{2}}$

Write the numerators and denominators in a common fraction.

${\tt \leadsto \dfrac{3 \times 3}{2 \times 1} - \dfrac{1}{2} = \dfrac{5 + 3}{2}}$

Multiply the fractions on LHS and add the fractions on RHS.

${\tt \leadsto \dfrac{9}{2} - \dfrac{1}{2} = \dfrac{8}{2}}$

Write both numerators with a common denominator on LHS.

${\tt \leadsto \dfrac{9 - 1}{2} = \dfrac{8}{2}}$

Write the obtaining fraction.

${\tt \leadsto \dfrac{8}{2} = \dfrac{8}{2}}$

So,

${\sf \leadsto LHS = RHS}$

$\:$

Hence verified !!