Respuesta :
Answer:
[tex]x=\frac{50}{59}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5}x-3 \frac{3}{4} x=2 \frac{1}{2}[/tex]
Convert the mixed fraction into improper fraction
[tex]3 \frac{3}{4}=\frac{3 \cdot 4+3}{4} =\frac{15}{4}[/tex]
[tex]2\frac{1}{2}=\frac{2 \cdot 2+1}{4} =\frac{5}{4}[/tex]
[tex]\frac{4}{5}x-\frac{15}{4}x=\frac{5}{2}[/tex]
LCD is 20. multiply the first fraction by 4 and second fraction by 5
multiply the right hand side fraction by 10 to get LCD 20
[tex]\frac{16}{20}x-\frac{75}{20}x=\frac{50}{20}[/tex]
Combine like terms
[tex]\frac{59}{20}x=\frac{50}{20}[/tex]
Both sides have same denominator
so we equate the numerators
[tex]59x= 50[/tex]
Divide both sides by 59
[tex]x=\frac{50}{59}[/tex]
