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

1.	Solve the equation : 3(y – 5) – 16y = 12 – 2(y – 3)
Answer» 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. ____________________________________ 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!

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