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 $36$.Read More

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 $-5$.Read More

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:$\frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2}{3}-t$.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 $2$.Read More

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 $\frac{7}{5}$.Read More

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:$15(y-4)-2(y-9)+5(y+6)=0$.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:$3(5 z-7)-2(9 z-11)=4(8 z-13)-17$.To do:We have to solve the given linear equation.Solution: $3(5 z-7)-2(9 z-11)=4(8 z-13)-17$This implies, $3(5z)-3(7)-2(9z)-2(-11)=4(8z)-4(13)-17$$15z-21-18z+22=32z-52-17$$-3z+1=32z-69$$32z+3z=69+1$$35z=70$$z =\frac{70}{35}$$z = 2$The value of $z$ is $2$. Read More

Given:$0.25(4 f-3)=0.05(10 f-9)$.To do:We have to solve the given linear equation.Solution: $0.25(4 f-3)=0.05(10 f-9)$This implies,$0.25(4 f)-0.25(3)=0.05(10 f)-0.05(9)$$f-0.75=0.5f-0.45$$f-0.5f=0.75-0.45$$0.5f=0.30$$f =\frac{0.3}{0.5}$$f = \frac{3}{5}$$f=0.6$The value of $f$ is $0.6$. 

Given:\( \frac{9 x}{7-6 x}=15 \)To do: We have to solve the given equation.Solution:$ \frac{9 x}{7-6 x}=15$$\Rightarrow 9x=15 \times(7-6x)$                [On cross multiplication]$\Rightarrow 9x=105-90x$$\Rightarrow 9x+90x=105$$\Rightarrow 99x=105$$\Rightarrow x=\frac{105}{99}$$\Rightarrow x=\frac{35}{33}$The value of $x$ is $\frac{35}{33}$.