Question

solve:
$\frac{x}{2}+5 = \frac{x}{3} + 7$
​

Answer 1

$\dashrightarrow \tt \red{ Solution: - }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \small\tt{ \frac{x}{2} + 5 = \frac{x}{3} + 7 }$

$\dashrightarrow \tt{ \frac{x }{2} + \frac{5 \times 2}{1 \times 2} = \frac{x}{3} + \frac{7 \times 3}{1 \times 3} }$

$\dashrightarrow \tt{ \frac{x }{2} + \frac{10}{2} = \frac{x}{3} + \frac{21}{3} }$

$\dashrightarrow\tt{ \frac{x + 10}{2} = \frac{x + 21}{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \small \tt \red{ Do \: Cross \: Multiplication}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \small \tt{3(x + 10) = 2(x + 21) }$

$\dashrightarrow \small \tt{3x + 30 = 2x + 42 }$

$\dashrightarrow \small \tt{3x - 2x= 42 - 30}$

$\boxed{ \underline{\dashrightarrow \small \tt{x = 12}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \small \tt \red{Verification(Optional):-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \tt{ \frac{x}{2} + 5 = \frac{x}{3} + 7 }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \tt \red{ First \: Solve \: LHS}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow\tt{ \frac{x}{2} + 5 }$

$\dashrightarrow\tt{ \frac{12}{2} + 5 }$

$\dashrightarrow \tt{ \frac{12}{2} + \frac{5 \times 2}{1 \times 2} }$

$\dashrightarrow\tt{ \frac{12}{2} + \frac{10}{2} }$

$\dashrightarrow\tt{ \frac{22}{2} }$

$\dashrightarrow \tt{ \cancel\frac{22}{2} }$

$\dashrightarrow \tt{ 11 }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \small \tt \red{ Now \: Solve \: RHS}$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow\tt{ \frac{x}{3} + 7}$

$\dashrightarrow\tt{ \frac{12}{3} + 7}$

$\dashrightarrow\tt{ \frac{12}{3} + \frac{7 \times 3}{1 \times 3}}$

$\dashrightarrow\tt{ \frac{12}{3} + \frac{21}{ 3} }$

$\dashrightarrow \tt{ \frac{33}{3} }$

$\dashrightarrow \tt{ \cancel\frac{33}{3} }$

$\dashrightarrow \tt{ 11 }$

$\: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dashrightarrow \small \tt \red{LHS = RHS}$

$\dashrightarrow \small \tt \red{Hence \: Verified}$