Question

If (0.4z-3)/(1.5z+9)=-7/5 then what us the value of z.

Answer 1

Answer :-

z = - 3.84

Solution :-

$\sf \dfrac{0.4z - 3}{1.5z + 9} = - \dfrac{7}{5}$

By Cross multiplication

$\sf (0.4z - 3)5= - 7(1.5z + 9)$

It can be written as

$\sf \left( \dfrac{4z}{10} - 3 \right)5 = - 7\left( \dfrac{15z}{10} + 9\right)$

$\sf \left( \dfrac{4z}{10}\right)5 -3(5) = - 7\left( \dfrac{15z}{10}\right) - 7(9)$

$\sf \dfrac{20z}{10} - 15 = - \dfrac{105z}{10} - 63$

$\sf \dfrac{20z}{10} + \dfrac{105z}{10} = - 63 + 15$

$\sf \dfrac{20z + 105z}{10} = - 48$

$\sf \dfrac{125z}{10} = - 48$

$\sf 125z= - 48(10)$

$\sf 125z= - 480$

$\sf z = - \dfrac{480}{125}$

$\sf z = - \dfrac{480 \div 5}{125 \div 5}$

$\sf z = - \dfrac{96}{25}$

$\sf z = - 3.84$

Verification :-

$\sf \dfrac{0.4z - 3}{1.5z + 9} = - \dfrac{7}{5}$

$\sf \implies \dfrac{0.4( - 3.84) - 3}{1.5 (-3.84) + 9} = - \dfrac{7}{5}$

$\sf \implies \dfrac{ - 1.536 - 3}{ - 5.76 + 9} = - \dfrac{7}{5}$

$\sf \implies \dfrac{ - 4.536 }{3.24} = - \dfrac{7}{5}$

$\sf \implies \dfrac{ - \frac{4536}{100} }{ \frac{3240}{100} } = - \dfrac{7}{5}$

$\sf \implies - \dfrac{4536}{1000} \times \dfrac{1000}{3240} = - \dfrac{7}{5}$

$\sf \implies - \dfrac{4536}{1} \times \dfrac{1}{3240} = - \dfrac{7}{5}$

$\sf \implies - \dfrac{4536}{3240} = - \dfrac{7}{5}$

$\sf \implies - \dfrac{4536 \div 648}{3240 \div 648} = - \dfrac{7}{5}$

$\sf \implies - \dfrac{7}{5}= - \dfrac{7}{5}$