## Solve each of the following equations and also check your results in each case:(i) $\frac{45-2x}{15}-\frac{4x+10}{5}=\frac{15-14x}{9}$(ii) $\frac{5(7x+5)}{3}-\frac{23}{3}=13-\frac{4x-2}{3}$

Updated on 13-Apr-2023 23:12:26
Given:The given equations are:(i) $\frac{45-2x}{15}-\frac{4x+10}{5}=\frac{15-14x}{9}$(ii) $\frac{5(7x+5)}{3}-\frac{23}{3}=13-\frac{4x-2}{3}$To do:We have to solve the given equations and check the results.Solution:To check the results we have to find the values of the variables and substitute them in the equation. Find the value of LHS and the value of RHS and check whether both are equal.(i) The given equation is $\frac{45-2x}{15}-\frac{4x+10}{5}=\frac{15-14x}{9}$$\frac{45-2x}{15}-\frac{4x+10}{5}=\frac{15-14x}{9}On rearranging, we get, \frac{45-2x}{15}-\frac{4x+10}{5}-\frac{15-14x}{9}=0LCM of denominators 15, 5 and 9 is 45$$\frac{(45-2x)\times3-(4x+10)\times9-(15-14x) \times5}{45}=0$$\frac{3(45)-3(2x)-9(4x)-9(10)-5(15)+5(14x)}{45}=0$$\frac{135-6x-36x-90-75+70x}{45}=0$$\frac{135-165-42x+70x}{45}=0$$\frac{-30+28x}{45}=0$On cross multiplication, we get, $28x-30=45(0)$$28x-30=0$$28x=30$$x=\frac{30}{28}$$x=\frac{15}{14}$Verification:LHS $=\frac{45-2x}{15}-\frac{4x+10}{5}$$=\frac{45-2(\frac{15}{14})}{15}-\frac{4(\frac{15}{14})+10}{5}$$=\frac{45-\frac{15}{7}}{15}-\frac{\frac{30}{7}+10}{5}$$=\frac{45\times7-15}{7\times15}-\frac{30+10\times7}{7\times5}$$=\frac{315-15}{105}-\frac{30+70}{35}$$=\frac{300}{105}-\frac{100}{35}$$=\frac{60}{21}-\frac{20}{7}$$=\frac{60-20\times3}{21}$$=\frac{60-60}{21}$$=0RHS =\frac{15-14x}{9}$$=\frac{15-14(\frac{15}{14})}{9}$$=\frac{15-15}{9}$$=0$LHS $=$ RHSHence verified.(ii) The given equation is $\frac{5(7x+5)}{3}-\frac{23}{3}=13-\frac{4x-2}{3}$$\frac{5(7x+5)}{3}-\frac{23}{3}=13-\frac{4x-2}{3}On rearranging, we get, \frac{5(7x+5)}{3}+\frac{4x-2}{3}=\frac{23}{3}+13LCM of 3 and 1 is 3$$\frac{5(7x)+5(5)+4x-2}{3}=\frac{23+13\times3}{3}$$\frac{35x+25+4x-2}{3}=\frac{23+39}{3}$$\frac{39x+23}{3}=\frac{62}{3}$On cross multiplication, we get, $39x+23=62$$39x=62-23$$39x=39$$x=\frac{39}{39}$$x=1$Verification:LHS $=\frac{5(7x+5)}{3}-\frac{23}{3}$$=\frac{5(7(1)+5)}{3}-\frac{23}{3}$$=\frac{5(7+5)}{3}-\frac{23}{3}$$=\frac{5(12)}{3}-\frac{23}{3}$$=\frac{60}{3}-\frac{23}{3}$$=\frac{60-23}{3}$$=\frac{37}{3}$RHS $=13-\frac{4x-2}{3}$$=13-\frac{4(1)-2}{3}$$=13-\frac{4-2}{3}$$=13-\frac{2}{3}$$=\frac{13\times3-2}{3})$$=\frac{39-2}{3}$$=\frac{37}{3}$LHS $=$ RHSHence ... Read More

## Solve each of the following equations and also check your results in each case:(i) $\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$(ii) $\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}=\frac{8x+19}{18}$

Updated on 13-Apr-2023 23:11:29
Given:The given equations are:(i) $\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$(ii) $\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}=\frac{8x+19}{18}$To do:We have to solve the given equations and check the results.Solution:To check the results we have to find the values of the variables and substitute them in the equation. Find the value of LHS and the value of RHS and check whether both are equal.(i) The given equation is $\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$$\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}LCM of denominators 3x and 2x is 6x$$\frac{2\times2-3\times3}{6x}=\frac{1}{12}$$\frac{4-9}{6x}=\frac{1}{12}$$\frac{-5}{6x}=\frac{1}{12}$On cross multiplication, we get, $-5\times12=1\times6x$$6x=-60$$x=\frac{-60}{6}$$x=-10Verification:LHS =\frac{2}{3x}-\frac{3}{2x}$$=\frac{2}{3(-10)}-\frac{3}{2(-10)}$$=\frac{2}{-30}-\frac{3}{-20}$$=\frac{-1}{15}-(\frac{-3}{20}$$=\frac{-1}{15}+\frac{3}{20}$$=\frac{-1\times4+3\times3}{60}$          (LCM of $15$ and $20$ is $60$)$=\frac{-4+9}{60}$$=\frac{5}{60}$$=\frac{1}{12}$RHS $=\frac{1}{12}$LHS $=$ RHSHence verified.(ii) The given equation is $\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}=\frac{8x+19}{18}$$\frac{4x}{9}+\frac{1}{3}+\frac{13x}{108}=\frac{8x+19}{18}On rearranging, we get, \frac{4x}{9}+\frac{13x}{108}-\frac{8x+19}{18}=-\frac{1}{3}LCM of 9, 108 and 18 is 108$$\frac{4x \times 12+13x \times1- (8x+19)\times6}{108}=-\frac{1}{3}$$\frac{48x+13x-48x-114}{108}=-\frac{1}{3}$$\frac{13x-114}{108}=-\frac{1}{3}$On ... Read More

## Solve each of the following equations and also check your results in each case:(i) $\frac{9x+7}{2}-(x-\frac{(x-2)}{7})=36$(ii) $0.18(5x-4)=0.5x+0.8$

Updated on 13-Apr-2023 23:10:16

## Solve each of the following equations and also check your results in each case:(i) $\frac{(3a-2)}{3}+\frac{(2a+3)}{2}=a+\frac{7}{6}$(ii) $x-\frac{(x-1)}{2}=1-\frac{(x-2)}{3}$

Updated on 13-Apr-2023 23:08:12

## Solve each of the following equations and also check your results in each case:(i) $\frac{7y+2}{5}=\frac{6y-5}{11}$(ii) $x-2x+2-\frac{16}{3}x+5=3-\frac{7}{2}x$

Updated on 13-Apr-2023 23:05:12