Question

Solve the following equation:

Answer 1

What is a linear equation?

- A equation of degree 1 is called linear equation.

Given,

equation:

$\frac{2}{3} x =\frac{3}{8} x +\frac{7}{12}$

To find,

The value of x.

Main solution :

This is a linear equation in one variable x.

Solving for x using transposition:

$\frac{2}{3} x =\frac{3}{8} x +\frac{7}{12}$

Now, transposing 3x/8 to LHS ( left hand side ) of the equation .

Remember :-

When transposing from one side to another side in an equation-

+ changes to -

- changes to +

× changes to ÷

÷ changes to ×

Using these laws, we get :

$\frac{2}{3} x -\frac{3}{8} x =\frac{7}{12}$

Taking LCM on LHS.

LCM of 3 and 8 is 24

$\frac{16x-9x}{24}=\frac{7}{12}$

$\frac{7x}{24} =\frac{7}{12}$

Transposing 24 to RHS ,

$7x =\frac{7 \times 24}{12}$

$7x = 14$

Transposing 7 to RHS to get the value of x,

$x =\frac{14}{7}$

$x = 2$

Answer : The value of x is 2.

Answer 2

Hello here is your Answer!!

Topic:- Algebraic Expression!!

Question!!!

$\bold{ \fbox{ \frac{2}{3} x = \frac{3}{8} x + \frac{7}{12}}}$

Arrange in particular form!!

To Solve By Arrangements method!!

$\bold{ \frac{2}{3} x - \frac{3}{8}x = \frac{7}{12}} \\ \\ \\ \implies \frac{16x - 9x}{24} = \frac{7}{12} \\ \\ \\ \implies \frac{16x - 9x}{1} = \frac{7}{ \cancel12} \times \cancel 24 \\ \\ \\ \implies16x - 9x = 14 \\ \\ \implies7x = 14 \\ \\ \\ \implies \: x = \frac{ \cancel14}{ \cancel7} \\ \\ x = 2$


Verify the Answer!!



$\implies \bold{ \fbox{ \frac{2}{3} x = \frac{3}{8} x + \frac{7}{12}}} \\ \\ \implies \bold{ \fbox{ \frac{2}{3} (2) = \frac{3}{8}(2) + \frac{7}{12}}} \\ \\ \implies \frac{4}{3} = \frac{6}{8} + \frac{7}{12} \\ \\ \\ \implies \frac{4}{3} = \frac{18 + 14}{24} \\ \\ \implies \frac{4}{3} = \frac{ \cancel32}{ \cancel24} \\ \\ \\ \\ \bold{ \fbox{hence \ll{ \frac{4}{3} = \frac{4}{3}} \ll}}verified$