Question

Solve the following linear equations. x/2-1/5=x/3+1/4 ​

Answer 1

Answer:

Given,

2

x

−

5

1

=

3

x

+

4

1

The denominators on two sides are 2,3,4 and 5.

Their LCM is 60.

Multiplying both sides by 60, we get

60×(

2

x

−

5

1

)=60×(

3

x

+

4

1

)

⇒60×

2

x

−60×

5

1

=60×

3

x

+60×

4

1

⇒30x−12=20x+15

⇒30x−20x=15+12

⇒10x=27

⇒x=

10

27

⇒x=2.7

Answer 2

Answer:

x = $\frac{27}{10}$  

Step-by-step explanation:

$\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}$   (used the butterfly method)

12 (5x - 2) = 10 (4x + 3)

60x - 24 = 40x + 30         (used the distributive property)

60x - 40x - 24 = 30         ( transfer 40 x to the left side)

60x - 40x = 30 + 24   (transfer 24 to the right, minus to add, add to minus)

20x = 54                     (add and minus)

x = $\frac{54}{10}$                            ( move the 20 into the right side)

x = $\frac{27}{10}$                            (simplify)