Question

3x-1/5-x/7=3. Solve the equation ( find the value of x) and also check it .

Answer 1

${\huge{\underline{\sf {\orange{Question :}}}}}$

[$\frac{3x \: - \: 1}{5} - \frac{x}{7} = 3$ ] $\:\:$Solve the equation (find x) and verify it.

${\huge{\underline{\sf {\pink{Answer :}}}}}$

$\boxed{ x \: = \: 7 }$

${\huge{\underline{\sf {\green{Explanation :}}}}}$

$\frac{3x \: - \: 1}{5} - \frac{x}{7} = 3$

Taking LCM of 7 and 5 = 35,

➣ $\frac{7(3x - 1) \: - \: 5(x)}{35} = 3$

Transposing 35 to the other side,

➣ $(21x - 7) - 5x = 35 \times 3$

➣ $21x \: - \: 7 \: - \: 5x \: = 105$

Transposing 7 to the other side,

➣ $16x \: = 105 \: + \: 7$

➣ $16x \: = \: 112$

Transposing 16,

➣ $x \: = \: \frac{112}{16}$

➣ $x \: = \: 7$

$\: \:$

$\: \: \:$

Verification :

Putting x = 7 in $\frac{(3x \: - \: 1) }{5} - \frac{x}{7}$

LHS

➣ $\frac{(3 \times 7 \: - 1) }{5} - \frac{7}{7}$

➣ $\frac{21 \: - \: 1}{5} - 1$

➣ $\frac{20}{5} - 1$

➣ $4 \: - \: 1$

➣ $3$

= RHS

So, LHS = RHS (Proved)

Answer 2

$\large \bf \to3x - \frac{1}{5} - \frac{x}{7} = 3 \\ \boxed{ \rm{}taking \: \: LCM \: \: of \: \: denominators} \\ \tt \leadsto\frac{105x - 7 -5 x}{35} = 3 \\ \boxed{ \small\rm{}performing \: \: calculation \: \: on \: \: numerator \: \: \& \: \: transposing \: \: 35 \: \: to \: \: RHS} \\ \leadsto \tt100x - 7 = 105 \\ \boxed{ \rm{transposing \: \: 7 \: \: to \: \: RHS} }\\ \leadsto \tt100x = 105 + 7 \\ \boxed{ \rm performing \: \: calculation \: \: in \: \: RHS}\\ \leadsto \tt100x = 112 \\ \boxed{ \rm dividing \: \: both \: \: sides \: \: by \: \: 100} \\\leadsto \tt \frac{100x}{100} = \frac{112}{100} \\\leadsto \tt x = \red{1.12}$