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1) 5x-1/3(x+1)=6(x+1/30)
2) 2x-(7-5x)/9x-(3+4x)=7/6
3) (2x+3)-(5x-7)/6x+11=-8/3​

Answer 1

2x-(7-5x)/9x-(3+4x)=7/6

Answer 2

Question:-

1) 5x-1/3(x+1)=6(x+1/30)

2) 2x-(7-5x)/9x-(3+4x)=7/6a

3) (2x+3)-(5x-7)/6x+11=-8/3

Solution:-

1)

It is a simple Equation with simple steps

5x−31(x+1)=6(x+301)

⇒5x−3x−31=6x+306

⇒5x−3x−6x=306+31

⇒315−x−18x=306+10

⇒−34x=3016

⇒−x=104

⇒x=−52

∴ Hence, the given equation is verified.

2)

We have,

2x – (7-5x) / 9x – (3+4x) = 7/6

(2x – 7 + 5x) / (9x – 3 – 4x) = 7/6

(7x – 7) / (5x – 3) = 7/6

By cross-multiplying we get,

6(7x – 7) = 7(5x – 3)

42x – 42 = 35x – 21

42x – 35x = -21 + 42

7x = 21

x = 21/7

= 3

Now let us verify the given equation,

2x – (7-5x) / 9x – (3+4x) = 7/6

(7x – 7) / (5x – 3) = 7/6

By substituting the value of ‘x’ we get,

(7(3) -7) / (5(3) – 3) = 7/6

(21-7) / (15-3) = 7/6

14/12 = 7/6

7/6 = 7/6

∴ Hence, the given equation is verified.

3)

We have,

((2x+3) – (5x-7))/(6x+11) = -8/3

By cross-multiplying we get,

3((2x+3) – (5x-7)) = -8(6x+11)

3(2x + 3 – 5x + 7) = -48x – 88

3(-3x + 10) = -48x – 88

-9x + 30 = -48x – 88

-9x + 48x = -88 – 30

39x = -118

x = -118/39

Now let us verify the given equation,

((2x+3) – (5x-7))/(6x+11) = -8/3

By substituting the value of ‘x’ we get,

((2(-118/39) + 3) – (5(-118/39) – 7)) / (6(-118/39) + 11) = -8/3

((-336/39 + 3) – (-590/39 – 7)) / (-708/39 + 11) = -8/3

(((-336+117)/39) – ((-590-273)/39)) / ((-708+429)/39) = -8/3

(-219+863)/39 / (-279)/39 = -8/3

644/-279 = -8/3

-8/3 = -8/3

∴ Hence, the given equation is verified.

Final Solution:-

1)⇒x=−52

2)⇒7/6 = 7/6

3)⇒-8/3 = -8/3

Hope it will help you ☺️