Answer:
The answer to the expression (x+2/3-x+1/5=x-3/4-1) is [tex]x=\frac{28}{5}[/tex]
Step-by-step explanation:
[tex]x+\frac{2}{3}-x+\frac{1}{5}=\frac{x-3}{4-1}\quad :\quad x=\frac{28}{5}\quad \left(\mathrm{Decimal}:\quad x=5.6\right)[/tex]
[tex]x+\frac{2}{3}-x+\frac{1}{5}=\frac{x-3}{4-1}[/tex]
[tex]\mathrm{Group\:like\:terms}\\x-x+\frac{2}{3}+\frac{1}{5}=\frac{x-3}{4-1}[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:x-x=0\\\frac{2}{3}+\frac{1}{5}=\frac{x-3}{4-1}[/tex]
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}3,\:5:\quad 15\\\mathrm{Prime\:factorization\:of\:}3:\quad 3\\\mathrm{Prime\:factorization\:of\:}5:\quad 5[/tex]
[tex]\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}3\mathrm{\:or\:}5\\=3\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:3\cdot \:5=15\\=15[/tex]
[tex]\\\\\\\frac{2}{3}=\frac{2\cdot \:5}{3\cdot \:5}=\frac{10}{15}\\\\\frac{1}{5}=\frac{1\cdot \:3}{5\cdot \:3}=\frac{3}{15}\\[/tex]
[tex]\frac{10+3}{15}=\frac{x-3}{4-1}[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:10+3=13\\\frac{13}{15}=\frac{x-3}{4-1}[/tex]
[tex]13\left(4-1\right)=15\left(x-3\right)[/tex]
[tex]39=15\left(x-3\right)\\15\left(x-3\right)=39\\\mathrm{Divide\:both\:sides\:by\:}15\\\frac{15\left(x-3\right)}{15}=\frac{39}{15}\\x-3=\frac{13}{5}\\x-3+3=\frac{13}{5}+3 = \frac{28}{5}[/tex]
Hope this helps!
Have a good morning. And happy Monday!
