Question

Solve the equation : 3(y – 5) – 16y = 12 – 2(y – 3)​

Answer 1

Answer:

answer

3y-15-16y =12-2y+6

-13y-15= 18-2y

18+15= 13y-2y

33=11y

y=3

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Answer 2

Answer :-

• The required number is -3.

Step-by-step explanation:

To Find :-

• Solve the equation

Given to solve :

• 3 ( y - 5 ) - 16y = 12 - 2 ( y - 3 )

Solution:

$\longrightarrow \: \sf{3 ( y - 5 ) - 16y = 12 - 2 ( y - 3 )}$

By simplifying both sides,

$\longrightarrow \: \sf{(3)(y) + (3)(-5) - 16y = 12 + (- 2)(y) + ( - 2)( - 3)}$

$\longrightarrow \: \sf{3y + ( - 15) - 16y = 12 + (- 2)(y) + ( - 2)( - 3)}$

$\longrightarrow \: \sf{3y + ( - 15) - 16y = 12 + ( - 2y) + ( - 2)( - 3)}$

$\longrightarrow \: \sf{3y + ( - 15) - 16y = 12 + ( - 2y) + 6}$

$\longrightarrow \: \sf{3y - 15 - 16y = 12 - 2y + 6}$

By evaluating the like terms step-by-step on L.H.S,

$\longrightarrow \: \sf{(3y - 16y) - 15 = 12 - 2y + 6}$

$\longrightarrow \: \sf{ - 13y - 15 = 12 - 2y + 6}$

By evaluating the like terms step-by-step on R.H.S,

$\longrightarrow \: \sf{ - 13y - 15 = - 2y + (12 + 6)}$

$\longrightarrow \: \sf{ - 13y - 15 = - 2y + 18}$

By transposing -15 to R.H.S and evaluating

$\longrightarrow \: \sf{ - 13y = - 2y + 18 + 15}$

$\longrightarrow \: \sf{ - 13y = - 2y + 33}$

By transposing -2y to L.H.S and evaluating,

$\longrightarrow \: \sf{ - 13y + 2y = 33}$

$\longrightarrow \: \sf{ - 11y = 33}$

$\longrightarrow \: \sf{y = \dfrac{- 33}{11}}$

$\longrightarrow \: \sf{y = \cancel{ \dfrac{- 33}{11}}}$

$\longrightarrow \: \underline{ \boxed{\sf{ \red{y = - 3}}}}$

Hence, The required number is -3.

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Now, Verification

• 3(y – 5) – 16y = 12 – 2(y – 3)

We have,

• L.H.S = 3(y – 5) – 16y
• R.H.S = 12 – 2(y – 3)

By putting the value of y on L.H.S and R.H.S seperately,

• L.H.S :-

$\longrightarrow \: \sf{3 ( y - 5 ) - 16y}$

By putting the value of y,

$\longrightarrow \: \sf{3 ( - 3 - 5 ) - (16)( - 3)}$

$\longrightarrow \: \sf{3 ( - 8) - (16)( - 3)}$

$\longrightarrow \: \sf{ - 24 - (16)( - 3)}$

$\longrightarrow \: \sf{ - 24 - ( - 48)}$

$\longrightarrow \: \sf{ - 24 + 48}$

$\longrightarrow \: { \boxed{ \sf{24}}}$

• R.H.S :-

$\longrightarrow \: \sf{12 - 2 ( y - 3 )}$

By putting the value of y,

$\longrightarrow \: \sf{12 - 2 ( - 3 - 3)}$

$\longrightarrow \: \sf{12 - 2 ( - 6)}$

$\longrightarrow \: \sf{12 + 12}$

$\longrightarrow \: \boxed{ \sf{24}}$

Now, we have,

• L.H.S = 24
• R.H.S = 24

∴ L.H.S = R.H.S

Hence, Verified!