Question

can you solve these 3 questions

Answer 1

There will be a value of a, considering the value of a as x,

Given that $\dfrac{2a}{7}+ \dfrac{a-1}{5}\:\: and\:\: \dfrac{a}{3}+ \dfrac{a}{7}$ will be equal on a value of a,

$\dfrac{2x}{7}+ \dfrac{x-1}{5} = \dfrac{x}{3}+ \dfrac{x}{7}$

$\dfrac{10x+7x-7}{5 \times 7} = \dfrac{7x+3x}{3 \times 7}$

$\dfrac{17x -7}{5 \times 7 } = \dfrac{10x}{3 \times 7}$

3 × 7 ( 17x - 7 ) = 5 × 7( 10 x )

3( 17x - 7 ) = 5( 10 x )

51x - 21 = 50x

51x - 50x = 21

x = 21

x = a = 21

Therefore, value of a should be 21  to make $\dfrac{2a}{7}+ \dfrac{a-1}{5}\:\: and\:\: \dfrac{a}{3}+ \dfrac{a}{7}$ equal.

6.

Given that $\dfrac{1}{5} ( 5x - 1 ) \:\: and \:\: \dfrac{1}{4} (8x + 1 )$ are equal.

$\dfrac{1}{5} ( 5x - 1 ) = \dfrac{1}{4} ( 8x + 1 )$

$\dfrac{5x -1 }{5} = \dfrac{8x+1}{4}$

4( 5x - 1 ) = 5( 8x + 1 )

20x - 4 = 40x + 5

- 4 - 5  = 40x - 20x

- 9 = 20 x

- 9 / 20 = x

Therefore the value of x is - 9 / 20

7.

If 3 is the root is ( 5x - 7 ) + 2( x - 3 ) = 2( x - 2 ) + ( 3x - 3 ), on putting x = 3 we will get 0 as result.

{ 5( 3 ) - 7 } + 2{ 3 - 3 } = 2{ 3 - 2 } + { 3( 3 ) - 3 }

{ 15 - 7 } + 2{ 0 } = 2{ 1 } + { 9 - 3 }

8 + 0 = 2 + 6

8 = 8

0 = 0

As result is 0, x = 3 is the root of If 3 is the root is ( 5x - 7 ) + 2( x - 3 ) = 2( x - 2 ) + ( 3x - 3 ).

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