Question

help please ::::::::::::::::​

Answer 1

Answer:

$\frac{-1}{2}$

Step-by-step explanation:

Let the Rational Number be

$x*\frac{5}{2} +\frac{2}{3} = \frac{-7}{12} \\\\\frac{5x}{2}= \frac{-7}{12} -\frac{2}{3}$

LCM of 12 and 3 = 12

$\frac{5x}{2}= \frac{-7}{12} -\frac{8}{12}\\\\\frac{5x}{2}= \frac{-7-8}{12} \\\\\frac{5x}{2}= \frac{-15}{12}\\\\5x= \frac{-15}{12}*2\\\\5x = \frac{-15}{6}\\\\x = \frac{-15}{6}*\frac{1}{5}\\\\x = \frac{-3}{6}\\\\x=\frac{-1}{2}$

Verification:

$\frac{-1}{2}*\frac{5}{2} + \frac{2}{3} = \frac{-7}{12} \\\\\frac{-5}{4} + \frac{2}{3} = \frac{-7}{12}$

LCM of 3 and 4 = 12

$\frac{-15}{12} + \frac{8}{12} = \frac{-7}{12} \\\\\frac{-15+8}{12} = \frac{-7}{12}\\\\\frac{-7}{12} = \frac{-7}{12}$