Respuesta :
Answer: x = –3
Step-by-step explanation:
Step 1:The given expression is [tex]4 \frac{2}{10}-\left(2 \frac{2}{5} x+5 \frac{1}{2}\right)=\frac{1}{2}\left(-3 \frac{2}{5} x+1 \frac{1}{5}\right)[/tex].
Step 2: Let us first convert the mixed fraction into improper fraction.
[tex]\Rightarrow \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]
Step 3: Remove the brackets.
[tex]\Rightarrow \frac{43}{10}-\frac{12}{5} x-\frac{11}{2}=\frac{-9}{5} x+\frac{3}{5}[/tex]
Step 4: Write x terms one side and constant terms one side and solving.
[tex]\Rightarrow \frac{9}{5} x-\frac{12}{5} x=\frac{3}{5}-\frac{43}{10}+\frac{11}{2}[/tex]
[tex]\Rightarrow \frac{-3}{5} x=\frac{6-43+55}{10}[/tex]
[tex]\Rightarrow \frac{-3}{5} x=\frac{18}{10}[/tex]
[tex]\Rightarrow x=\frac{18}{10} \times \frac{-5}{3}[/tex]
⇒ x = –3
Therefore, the value of x in the given expression is –3.
