Question

$x + 5 \div 7x = 2 \div 3$
Please tell me answer of this question​

Answer 1

Given:

The equation -

$\bf x + 5 \div 7x = 2 \div 3$

Also written as -

$\bf \dfrac{x + 5}{7x} = \dfrac{2}{3}$

What To Find:

We have to

• Solve the given equation.
• Find the value of x.

Solution:

$\bf \longrightarrow \dfrac{x + 5}{7x} = \dfrac{2}{3}$

Use the cross multiplication,

$\bf \longrightarrow 3(x + 5) = 2(7x)$

Solve the brackets,

$\bf \longrightarrow 3x + 15 = 14x$

Take 3x to RHS,

$\bf \longrightarrow 15 = 14x - 3x$

Subtract 3x from 14x,

$\bf \longrightarrow 15 = 11x$

Take 11 to LHS,

$\bf \longrightarrow \dfrac{15}{11} = x$

Verification:

$\bf \longrightarrow \dfrac{x + 5}{7x} = \dfrac{2}{3}$

Substitute the values,

$\bf \longrightarrow \dfrac{\dfrac{15}{11} + 5}{7 \times \dfrac{15}{11}} = \dfrac{2}{3}$

Solve the denominator in LHS,

$\bf \longrightarrow \dfrac{\dfrac{15}{11} + 5}{\dfrac{105}{11}} = \dfrac{2}{3}$

Solve the numerator in LHS,

$\bf \longrightarrow \dfrac{\dfrac{70}{11} \:}{\dfrac{105}{11}} = \dfrac{2}{3}$

Take the denominator like this,

$\bf \longrightarrow \dfrac{70}{11} \times \dfrac{11}{105}= \dfrac{2}{3}$

Cancel the elevens,

$\bf \longrightarrow \dfrac{70}{105}= \dfrac{2}{3}$

Cancel 70 and 105,

$\bf \longrightarrow \dfrac{2}{3}= \dfrac{2}{3}$

∵ LHS = RHS

∴ Hence, verified.

Final Answer:

∴ Thus, the value of x is $\bf \dfrac{15}{11}$ .

Answer 2

Solution :

Given :

x + 5/7x = 2/3

Explanation :

= x + 5/7x = 2/3

= 3(x + 5) = 7x × 2

= 3x + 15 = 7x × 2

= 3x + 15 = 14x

= 3x - 14x = -15

= -11x = -15

= x = -15/-11

= x = 15/11