Question

Solve for x.
13
=(5x+ 6)/8 +
(5x+4)/4​​

Answer 1

Given :

$\displaystyle {\frac{(5x+6)}{8}+\frac{(5x+4)}{4}}=13$

Solution :

Given that ,

$\implies \displaystyle {\frac{(5x+6)}{8}+\frac{(5x+4)}{4}}=13$

Cross Multiplying the terms,

$\implies \displaystyle {\frac{4(5x+6)+8(5x+4)}{8\times 4 }=13}$

$\implies \displaystyle {\frac{(20x+24)+(40x+32)}{32}=13}$

$\implies \displaystyle {20x+40x+24+32=13\times 32}$

$\implies \displaystyle {60x+56=416}$

$\implies \displaystyle {60x=416-56}$

$\implies \displaystyle {60x=360}$

$\implies \displaystyle {x=\dfrac{{\cancel{360}}^6}{{\cancel{60}}_1}}\Rightarrow \boxed{\displaystyle{x=6}}$

Verification :

$\implies \displaystyle {\frac{(5x+6)}{8}+\frac{(5x+4)}{4}}=13$

Substituting the value of x,

$\implies \displaystyle {\frac{(5(6)+6)}{8}+\frac{(5(6)+4)}{4}}=13$

$\implies \displaystyle \Big({\frac{30+6}{8}+\frac{30+4}{4}}\Big)=13$

$\implies \displaystyle \Big({\frac{{\cancel{36}}^9}{{\cancel{8}}_2}+\frac{{\cancel{34}}^{17}}{{\cancel{4}}_2}}\Big)=13$

$\implies \displaystyle {\frac{9+17}{2}}=13$

$\implies \displaystyle {\frac{{\cancel{26}}^{13}}{{\cancel{2}}_1}}=13$

$\implies 13 = 13$

$\sf Hence\:Verified$

Required Answer :

$\boxed{\boxed{\displaystyle \sf x=6\:in\:{\frac{(5x+6)}{8}+\frac{(5x+4)}{4}}=13}}$