Solve 4/5(1+10n)-2(4n-3)

$$\frac { 4 } { 5 } ( 1 + 10 n ) - 2 ( 4 n - 3 )$$

Evaluate

$$\frac{34}{5}=6.8$$

Solution Steps

Use the distributive property to multiply \frac{4}{5} by 1+10n.

$$\frac{4}{5}+\frac{4}{5}\times 10n-2\left(4n-3\right)$$

Express \frac{4}{5}\times 10 as a single fraction.

$$\frac{4}{5}+\frac{4\times 10}{5}n-2\left(4n-3\right)$$

Multiply 4 and 10 to get 40.

$$\frac{4}{5}+\frac{40}{5}n-2\left(4n-3\right)$$

Divide 40 by 5 to get 8.

$$\frac{4}{5}+8n-2\left(4n-3\right)$$

Use the distributive property to multiply -2 by 4n-3.

$$\frac{4}{5}+8n-8n+6$$

Combine 8n and -8n to get 0.

$$\frac{4}{5}+6$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{4}{5}+\frac{30}{5}$$

Since \frac{4}{5} and \frac{30}{5} have the same denominator, add them by adding their numerators.

$$\frac{4+30}{5}$$

Add 4 and 30 to get 34.

$$\frac{34}{5}$$

Factor

$$\frac{2 \cdot 17}{5} = 6\frac{4}{5} = 6.8$$

Solution Steps

Factor out \frac{2}{5}.

$$\frac{2\left(2\left(1+10n\right)-5\left(4n-3\right)\right)}{5}$$

Simplify.

$$\frac{34}{5}$$