Given:$15(y-4)-2(y-9)+5(y+6)=0$.To do:We have to solve the given linear equation.Solution: $15(y-4)-2(y-9)+5(y+6)=0$This implies,$15(y)-15(4)-2(y)-2(-9)+5(y)+5(6)=0$$15y-60-2y+18+5y+30=0$$18y-12=0$$18y=12$$y =\frac{12}{18}$$y = \frac{2}{3}$The value of $y$ is $\frac{2}{3}$. 

Given:$3(t-3)=5(2 t+1)$.To do:We have to solve the given linear equation.Solution: $3(t-3)=5(2 t+1)$This implies,$3(t)-3(3)=5(2t)+5(1)$$3t-9=10t+5$$10t-3t=-9-5$$7t=-14$$t =\frac{-14}{7}$$t = -2$The value of $t$ is $-2$.

Given:$m-\frac{m-1}{2}=1-\frac{m-2}{3}$.To do:We have to solve the given linear equation.Solution: $m-\frac{m-1}{2}=1-\frac{m-2}{3}$This implies,$m-\frac{m-1}{2}+\frac{m-2}{3}=1$$\frac{6(m) - 3( m-1) +2(m-2)}{6}=1$$6m-3m+3+2m-4= 1\times6$$5m-1= 6$$5m=6+1$$5m=7$$m =\frac{7}{5}$The value of $m$ is $\frac{7}{5}$.

Given:$\frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2}{3}-t$.To do:We have to solve the given linear equation.Solution: $\frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2}{3}-t$This implies,$\frac{3 t-2}{4}-\frac{2 t+3}{3}+t=\frac{2}{3}$$\frac{3(3t-2) - 4( 2t+3) +12(t)}{12}=\frac{2}{3}$$9t-6-8t-12+12t= \frac{2}{3}\times12$$13t-18= 2(4)$$13t=8+18$$13t=26$$t =\frac{26}{13}$$t = 2$The value of $t$ is $2$.

Given:$\frac{x-5}{3}=\frac{x-3}{5}$.To do:We have to solve the given linear equation.Solution: $\frac{x-5}{3}=\frac{x-3}{5}$This implies,$5(x-5) =3(x-3)$$5(x)-5(5)=3(x)-3(3)$$5x-25=3x-9$$5x-3x=-9+25$$2x=16$$x=\frac{16}{2}$$x=8$The value of $x$ is $8$. 

Given:$x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}$.To do:We have to solve the given linear equation.Solution: $x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}$This implies,$x-\frac{8x}{3}+\frac{5x}{2} =\frac{17}{6} -7$$\frac{6\times x-8x\times 2+5x\times3}{6}=\frac{17-7\times6}{6}$$\frac{6x-16x+15x}{6}=\frac{17-42}{6}$$5x=-25$$x=\frac{-25}{5}$$x=-5$The value of $x$ is $-5$.

Given:$\frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21$.To do:We have to solve the given linear equation.Solution: $\frac{n}{2}-\frac{3 n}{4}+\frac{5 n}{6}=21$This implies,$\frac{n(6) - 3n( 3) +5n(2)}{12}=21$$\frac{6n - 9n + 10n}{12}  = 21$$\frac{7n}{12}= 21$$n =21 \times \frac{12}{7}$$n =3 \times 12$$n = 36$The value of $n$ is $36$.

Given:$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$.To do:We have to solve the given linear equation.Solution: $\frac{x}{2} - \frac{1}{5} = \frac{x}{3}+\frac{1}{4}$This implies,$\frac{x}{2} -\frac{x}{3} =\frac{1}{4} +\frac{1}{5}$$\frac{3\times x-2\times x}{6}=\frac{1\times5+1\times4}{20}$$\frac{3x-2x}{6}=\frac{5+4}{20}$$\frac{x}{6}=\frac{9}{20}$$x=6\times\frac{9}{20}$$x=\frac{27}{10}$The value of $x$ is $\frac{27}{10}$.

Given :Aman's age is three times his son's age.10 years ago he was five times his son's age.To do :We have to find their present ages.Solution :Let the present age of his son be $x$.This implies, that Aman's present age $=3x$.10 years ago, the age of Aman is 5 times the age of his son.The age of his son 10 years ago $= x-10$The age of Aman 10 years ago $= 3x-10$Therefore, $3x-10=5(x-10)$$3x-10=5x-50$$5x-3x = 50-10$$2x = 40$$x = \frac{40}{2}$$x = 20$$3 x = 3 \times 20 = 60$The present age of Aman is 60 years and the present age of ... Read More

Given:A grand father is ten times older than his granddaughter.He is also 54 years older than her.To do: We have to find the present ages of Grand father and his grand daughter.Solution:Let the present age of the grand daughter be $a$The grand father is ten times older than his granddaughter.This implies, Present age of grand father $= 10a$Grand father is 54 years older than grand daughter. Therefore, Age of grand father $=$ Age of grand daughter $+ 54$$10a = a+54$$10a - a = 54$$9a = 54$$a = \frac{54}{9}$$a=6$Therefore, The present age of grand daughter $=a$$= 6$ yearsThe present age of grand father ... Read More