Melissa ran 6 2/5 miles north 2 3/4 west and 2 1/3 south how far did she run

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elenaabad18

29.06.2021

Mathematics

• for the first inequality:

$\dashrightarrow \: { \tt{3(a - 5x) < 1 + x}} \\ \\ { \tt{3a - 15x < 1 + x}} \\ \\ { \tt{3a < 1 + 16x}} \\ \\ { \boxed{ \tt{a = \frac{1 + 16x}{3} \: \: { \red{}} }}}$

• for the second inequality:

$\dashrightarrow \: { \tt{ \frac{2 - x}{2} 3 + 5(x - a) }} \\$

substitute for a:

${ \tt{ \frac{2 - x}{2} 3 + 5(x - \frac{1 + 16x}{3} ) }} \\ \\ { \tt{ \frac{2 - x}{2} 3 - \frac{5 + 80x}{3} }} \\ \\ { \tt{2 - x 6 - \frac{10 + 160x}{3} }} \\ \\ { \tt{6 - 3x 18 - 10 - 160x}} \\ \\ { \tt{157x 2}} \\ \\ { \tt{x \frac{2}{157} }}$

• substitute to get value of a: [ first inequality ]

${ \tt{a < \frac{1 + 16( \frac{2}{157}) }{3} }} \\ \\{ \boxed{ \tt{a < \frac{63}{157} }}}$

[ second inequality ]

${ \boxed{ \tt{a \frac{65}{157} }}}$

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