Answer:

1) x = 3

2) x = 18

Step-by-step explanation:

1) 4(2x-3) -37 = 5(4-3x)

Solution:-

LHS

4(2x-3) -37

8x-12 - 37

8x-49

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RHS

5(4-3x)

20 - 15x

----------------------------------

now for x :-

8x-49=20-15x

(now since the variable must always be positive)

8x +15x = 20+49

23x = 69

x = 69/23

(ans) x = 3

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VERIFICATION

4(2x-3) -37=5(4-3x)

(putting the value of x in the equation)

4{(2×3) - 3} -37 = 5{4-(3×3)}

4{6-3} -37 = 5{ 4- 9}

4×3 -37 = 5× -5

12 -37 = -25

-25 = -25

hence verified.

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2) 1/2x +1/3x = 15

firstly, taking the LCM of the denominator 2 and 3.

LCM= 6

therefore:-

{(1/2x)3} + {(1/3x)2} = 15

3/6x + 2/6x = 15

5/6x = 15

taking 6 to the RHS

5x = 15×6

x = 90/5

x = 18

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VERIFICATION

1/2x +1/3x = 15

putting the value of x in the equation:-

{(1/2)18} + {(1/3)18} = 15

since 2 and 3 are divisible by 18:-

9+6 = 15

15= 15

hence verified.

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