Respuesta :
The value of x is –3.
Solution:
Given statement:
4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)
Let's convert this into algebraic expression.
[tex]$4\frac{3}{10} -\left(2\frac{2}{5}x+5\frac{1}{2}\right)=\frac{1}{2}\left(-3\frac{3}{5}x+1\frac{1}{5}\right)[/tex]
First convert mixed fraction into improper fraction.
[tex]$\frac{43}{10} -\left(\frac{12}{5}x+\frac{11}{2}\right)=\frac{1}{2}\left(-\frac{18}{5}x+\frac{6}{5}\right)[/tex]
[tex]$\frac{43}{10} -\frac{12}{5}x-\frac{11}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]
Now, take LCM and make the denominators same.
LCM of 2, 5, 10 = 10
[tex]$\frac{43}{10} -\frac{12\times2}{5\times2}x-\frac{11\times5}{2\times5}=-\frac{18}{10}x+\frac{6}{10}[/tex]
[tex]$\frac{43}{10} -\frac{24}{10}x-\frac{55}{10}=-\frac{18}{10}x+\frac{6}{10}[/tex]
Arrange like terms one side of the equation.
[tex]$\frac{18}{10}x -\frac{24}{10}x=\frac{6}{10}-\frac{43}{10}+\frac{55}{10}[/tex]
[tex]$\frac{18x-24x}{10} =\frac{6-43+55}{10}[/tex]
[tex]$\frac{-6x}{10} =\frac{18}{10}[/tex]
[tex]$-6x=\frac{18\times10}{10}[/tex]
[tex]$-6x=18[/tex]
Divide both sides of the expression by –6, we get
⇒ x = –3
Hence the value of x is –3.
