Respuesta :
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]
Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]
Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].
- [tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$}[/tex]
Subtract 8/5 from both sides.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}[/tex]
Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}[/tex]
Subtract 8 from 4 to get -4.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$}[/tex]
Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].
- [tex]\large\displaystyle\text{$\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$}[/tex]
Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
- [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}[/tex]
- [tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}[/tex]
Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.
- [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x=\frac{1}{2} \end{gathered}$}}[/tex]
- Good luck in your studies
