Question

4/10x - 2x + 8/5 = 4/5

Answer 1

$\large\displaystyle\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$

Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.

• $\large\displaystyle\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$

Combine $\bf{\frac{2}{5}x }$ and -2x to get $\bf{-\frac{8}{5}x}$.

• $\large\displaystyle\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$

Subtract 8/5 from both sides.

• $\large\displaystyle\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$

Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.

• $\large\displaystyle\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$

Subtract 8 from 4 to get -4.

• $\large\displaystyle\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$

Multiply both sides by $\bf{-\frac{5}{8}}$, the reciprocal of $\bf{-\frac{5}{8}}$.

• $\large\displaystyle\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$

Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

• $\large\displaystyle\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$
• $\large\displaystyle\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$

Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.

• $\boxed{\large\displaystyle\begin{gathered}\sf x=\frac{1}{2} \end{gathered}}$

• Good luck in your studies