Question

$$8x(3)+1+(-6)-(-x); 8x-9-6\times2+4\times(-8); \frac{4}{9}\div\frac{2}{5}+\frac{8}{9}\cdot-(\frac{-2}{5})$$

Answer

24*x+1-6+x;8*x-9-12+4*-8;4/9/(2/5)+16/45

Solution


Remove parentheses.
\[\begin{aligned}&8x\times 3+1-6-(-x)\\&8x-9-6\times 2+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{8}{9}\times \frac{2}{5}\end{aligned}\]
Simplify  \(8x\times 3\)  to  \(24x\).
\[\begin{aligned}&24x+1-6-(-x)\\&8x-9-6\times 2+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{8}{9}\times \frac{2}{5}\end{aligned}\]
Simplify  \(6\times 2\)  to  \(12\).
\[\begin{aligned}&24x+1-6-(-x)\\&8x-9-12+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{8}{9}\times \frac{2}{5}\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&24x+1-6-(-x)\\&8x-9-12+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{8\times 2}{9\times 5}\end{aligned}\]
Simplify  \(8\times 2\)  to  \(16\).
\[\begin{aligned}&24x+1-6-(-x)\\&8x-9-12+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{16}{9\times 5}\end{aligned}\]
Simplify  \(9\times 5\)  to  \(45\).
\[\begin{aligned}&24x+1-6-(-x)\\&8x-9-12+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{16}{45}\end{aligned}\]
Remove parentheses.
\[\begin{aligned}&24x+1-6+x\\&8x-9-12+4\times -8\\&\frac{\frac{4}{9}}{\frac{2}{5}}+\frac{16}{45}\end{aligned}\]