Question

Find the value of x if x/4+2/5=x/2-1​

Answer 1

Given:

The equation -

$\bf \longmapsto \: \dfrac{x}{4} + \dfrac{2}{5} = \dfrac{x}{2-1}$

What To Find:

We have to

• Find the value of x.

Solution:

$\sf \longmapsto \: \dfrac{x}{4} + \dfrac{2}{5} = \dfrac{x}{2-1}$

Take the LCM of 4 and 5 i.e 20 in LHS,

$\sf \longmapsto \: \dfrac{x \times 5}{4 \times 5} + \dfrac{2\times 4}{5 \times 4} = \dfrac{x}{2-1}$

Multiply both the numerator and denominator,

$\sf \longmapsto \: \dfrac{5x}{20} + \dfrac{8}{20} = \dfrac{x}{2-1}$

Add the fractions in LHS,

$\sf \longmapsto \: \dfrac{5x+8}{20} = \dfrac{x}{2-1}$

Subtract 1 from 2 in the denominator in RHS,

$\sf \longmapsto \: \dfrac{5x+8}{20} = \dfrac{x}{1}$

Use cross multiplication,

$\sf \longmapsto \: 5x+8 = 20x$

Take 5x to RHS from LHS,

$\sf \longmapsto \: 8 = 20x - 5x$

Subtract 20x to 5x in RHS,

$\sf \longmapsto \: 8 = 15x$

Take 15 to LHS,

$\sf \longmapsto \: \dfrac{8}{15} = x$

Verification:

$\sf \longmapsto \: \dfrac{x}{4} + \dfrac{2}{5} = \dfrac{x}{2-1}$

Take the LCM of 4 and 5,

$\sf \longmapsto \: \dfrac{x \times 5}{4 \times 5} + \dfrac{2\times 4}{5 \times 4} = \dfrac{x}{2-1}$

Multiply the numerator and denominator,

$\sf \longmapsto \: \dfrac{5x}{20} + \dfrac{8}{20} = \dfrac{x}{2-1}$

Add the fractions,

$\sf \longmapsto \: \dfrac{5x+8}{20} = \dfrac{x}{2-1}$

Subtract 1 from 2 in the denominator,

$\sf \longmapsto \: \dfrac{5x+8}{20} = \dfrac{x}{1}$

Substitute the value of x,

$\sf \longmapsto \: \dfrac{5 \bigg(\dfrac{8}{15} \bigg) +8}{20} = \dfrac{\dfrac{8}{15}}{1}$

Cancel 5 and 15,

$\sf \longmapsto \: \dfrac{\dfrac{8}{3} +8}{20} = \dfrac{\dfrac{8}{15}}{1}$

Take the LCM of 1 and 3 i.e 3,

$\sf \longmapsto \: \dfrac{\dfrac{8}{3} + \dfrac{24}{3}}{20} = \dfrac{\dfrac{8}{15}}{1}$

Add the fractions,

$\sf \longmapsto \: \dfrac{\dfrac{32}{3}}{20} = \dfrac{\dfrac{8}{15}}{1}$

Divide the fraction by 20,

$\sf \longmapsto \: \dfrac{32}{3} \times \dfrac{1}{20} = \dfrac{\dfrac{8}{15}}{1}$

Cancel the numbers,

$\sf \longmapsto \: \dfrac{8}{3} \times \dfrac{1}{5} = \dfrac{\dfrac{8}{15}}{1}$

Multiply the fractions,

$\sf \longmapsto \: \dfrac{8}{15} = \dfrac{\dfrac{8}{15}}{1}$

Divide the fraction in RHS,

$\sf \longmapsto \: \dfrac{8}{15} = \dfrac{8}{15} \div 1$

Also written as,

$\sf \longmapsto \: \dfrac{8}{15} = \dfrac{8}{15} \times 1$

Multiply,

$\sf \longmapsto \: \dfrac{8}{15} = \dfrac{8}{15}$

∵ LHS = RHS

∴ Hence, verified.

Final Answer:

∴ Thus the value of x is 8/15.