Question

Solve for x: (2 – 7x)/(1 – 5x) = (3 + 7x)/(4 +5x) ​

Answer 1

${{\fcolorbox{red}{white}{ \fcolorbox{red}{white}{ \bf{ \color{black}{solution \: \: \: \: \: \: \:\: \:\:\: \: \: \: \: \: \: \: \: \: \: \: }}}}}}$

$\color{black}\bold</p><p>{ \frac{2 - 7x}{1 - 5x} = \frac{3 + 7x}{4 + 5x} }$

$\color{black}\bold</p><p>{ \mapsto \:(2 - 7x)(4 + 5x) = (3 + 7x)(1 - 5x }$

$\color{black}\bold</p><p>{ \mapsto \: 8 + 10x - 28x - 35 {x}^{2} = 3 - 15x + 7x - 35 {x}^{2} }$

$\color{black}\bold</p><p>{ \mapsto \: - 35 {x}^{2} + 35 {x}^{2} + 10x - 28x + 15x - 7x = 3 - 8 }$

$\color{black}\bold</p><p>{ \mapsto \: 10x - 28x + 15x - 7x = - 5}$

$\color{black}\bold</p><p>{ \mapsto \:10x + 15x - 28x - 7x = - 5 }$

$\color{black}\bold</p><p>{ \mapsto \:25x - 35x = - 5}$

$\color{black}\bold</p><p>{ \mapsto \: - 10x = - 5 }$

$\color{black}\bold</p><p>{ \mapsto \:x = \frac{ - 5}{ - 10} }$

$\color{black}\bold</p><p>{ \mapsto \:x = \frac{1}{2} }$

${ \boxed{∵x = \frac{1}{2} }}</p><p>$

${{\fcolorbox{red}{white}{ \fcolorbox{red}{white}{ \bf{ \color{black}{ \: \: \: \: \: \: verification \: \: \: \: \: \: \: \: \: \: }}}}}}$

$\color{black}\bold</p><p>{ LHS = \frac{2 - 7x}{1 - 5x} }$

$\color{black}\bold</p><p>{ = \frac{2 - 7 \times \frac{1}{2} }{1 - 5 \times \frac{1}{2} } }$

$\color{black}\bold</p><p>{ = 2 - 7 \times \frac{1}{2} \div 1 - 5 \times \frac{1}{2} }$

$\color{black}\bold</p><p>{ = 2 - \frac{7}{2} } \div 1 - \frac{5}{2}$

$\color{black}\bold</p><p>{ = \frac{4 - 7}{2} \div } \frac{2 - 5}{2}$

$\color{black}\bold</p><p>{ = \frac{ - 3}{2} \div \frac{ - 3}{2} }$

$\color{black}\bold</p><p>{ = \frac{ - 3}{2} \times \frac{2}{ - 3} }$

$\color{black}\bold</p><p>{ = 1}$

$\color{black}\bold</p><p>{ RHS = \frac{3 + 7x}{4 + 5x} }$

$\color{black}\bold{ = \frac{3 + 7 \times \frac{1}{2} }{4 + 5 \times \frac{1}{2} } }$

$\color{black}\bold{ = 3 + 7 \times \frac{1}{2} \div 4 + 5 \times \frac{1}{2} }$

$\color{black}\bold{ =3 + \frac{7}{2} \div 4 + \frac{5}{2} }$

$\color{black}\bold{ = \frac{6 + 7}{2} \div \frac{8 + 5}{2} }$

$\color{black}\bold{ = \frac{13}{2} \div \frac{13}{2} }$

$\color{black}\bold{ = \frac{13}{2} \times \frac{2}{13} }$

$\color{black}\bold{ = 1}$

${ \boxed{∵verified }}</p><p>$