Question

solve each of equations 2‌x-1/3 + 6x-2/5 =1/3 (ans x=4/7)​

Answer 1

$\bigstar{ \underline{\sf\large\red{Given}}} : - -$

• $\bm{\dfrac{2x - 1}{3} + \frac{6x - 2}{5} = \frac{1}{3} }$

$\bigstar{ \underline{\sf\large\pink{To \: Find }}} : - -$

• solve each of the equations

$\bigstar{ \underline{\sf\large\green{Solution}}} : - -$

we have

$\bf \: \frac{2x - 1}{3} + \frac{6x - 2}{5} = \frac{1}{3}$

now we will find LCM of denominators

LCM of 3 & 5 = 15

$\longmapsto \tt \: \dfrac{5(2x - 1) + 3(6x - 2)}{15} = \dfrac{1}{3} \\ \\ \\ \longmapsto \sf \: \frac{10x - 5 +18x - 6 }{15} = \frac{1}{3} \\ \\ \\ \longmapsto \tt \frac{10x - 18x + 5 - 6}{15} = \frac{1}{3} \\ \\ \\ \longmapsto \tt \frac{8x + 1}{15} = \frac{1}{3}$

now cross multiply

$\longmapsto \tt \:3( 8x + 1) = 1(15) \\ \\ \\ \longmapsto \tt24x + 3 = 15 \\ \\ \\ \longmapsto \tt24x = 15 - 3 \\ \\ \\ \longmapsto \tt 24x = - 12 \\ \\ \\ \longmapsto \tt \: x = -\cancel \frac{24}{12} \\ \\ \\ \qquad \qquad \boxed{ \longmapsto \tt \: x = - \frac{2}{1} }$

hence the x = - 1/2

_____________________________

note : --- your book answers is wrong

Answer 2

Answer:

$\bigstar{ \underline{\sf\large\red{Given}}} : - -★Given:−−</p><p></p><p>\begin{gathered} \bm{\dfrac{2x - 1}{3} + \frac{6x - 2}{5} = \frac{1}{3} } \\ \end{gathered}32x−1+56x−2=31</p><p></p><p>\bigstar{ \underline{\sf\large\pink{To \: Find }}} : - -★ToFind:−−</p><p></p><p>solve each of the equations</p><p></p><p>\bigstar{ \underline{\sf\large\green{Solution}}} : - -★Solution:−−</p><p></p><p>we have</p><p></p><p>\begin{gathered} \bf \: \frac{2x - 1}{3} + \frac{6x - 2}{5} = \frac{1}{3} \\ \end{gathered}32x−1+56x−2=31</p><p></p><p>now we will find LCM of denominators</p><p></p><p>LCM of 3 & 5 = 15</p><p></p><p>\begin{gathered} \longmapsto \tt \: \dfrac{5(2x - 1) + 3(6x - 2)}{15} = \dfrac{1}{3} \\ \\ \\ \longmapsto \sf \: \frac{10x - 5 +18x - 6 }{15} = \frac{1}{3} \\ \\ \\ \longmapsto \tt \frac{10x - 18x + 5 - 6}{15} = \frac{1}{3} \\ \\ \\ \longmapsto \tt \frac{8x + 1}{15} = \frac{1}{3} \end{gathered}⟼155(2x−1)+3(6x−2)=31⟼1510x−5+18x−6=31⟼1510x−18x+5−6=31⟼158x+1=31</p><p></p><p>now cross multiply</p><p></p><p>\begin{gathered} \longmapsto \tt \:3( 8x + 1) = 1(15) \\ \\ \\ \longmapsto \tt24x + 3 = 15 \\ \\ \\ \longmapsto \tt24x = 15 - 3 \\ \\ \\ \longmapsto \tt 24x = - 12 \\ \\ \\ \longmapsto \tt \: x = -\cancel \frac{24}{12} \\ \\ \\ \qquad \qquad \boxed{ \longmapsto \tt \: x = - \frac{2}{1} }\end{gathered}⟼3(8x+1)=1(15)⟼24x+3=15⟼24x=15−3⟼24x=−12⟼x=−1224⟼x=−12</p><p></p><p>hence the x = - 1/2</p><p></p><p>_____________________________</p><p></p><p>note : --- your book answers is wrong</p><p></p><p>$