Solve 1/2 * (4m - 8n) + 4(2m - 1/4 * n) = | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{1}{2}(4m-8n)+4(2m-\frac{1}{4}n)=$$

Evaluate

$10m-5n$

Solution Steps

Use the distributive property to multiply $\frac{1}{2}$ by $4m-8n$.

$$\frac{1}{2}\times 4m+\frac{1}{2}\left(-8\right)n+4\left(2m-\frac{1}{4}n\right)$$

Multiply $\frac{1}{2}$ and $4$ to get $\frac{4}{2}$.

$$\frac{4}{2}m+\frac{1}{2}\left(-8\right)n+4\left(2m-\frac{1}{4}n\right)$$

Divide $4$ by $2$ to get $2$.

$$2m+\frac{1}{2}\left(-8\right)n+4\left(2m-\frac{1}{4}n\right)$$

Multiply $\frac{1}{2}$ and $-8$ to get $\frac{-8}{2}$.

$$2m+\frac{-8}{2}n+4\left(2m-\frac{1}{4}n\right)$$

Divide $-8$ by $2$ to get $-4$.

$$2m-4n+4\left(2m-\frac{1}{4}n\right)$$

Use the distributive property to multiply $4$ by $2m-\frac{1}{4}n$.

$$2m-4n+8m+4\left(-\frac{1}{4}\right)n$$

Cancel out $4$ and $4$.

$$2m-4n+8m-n$$

Combine $2m$ and $8m$ to get $10m$.

$$10m-4n-n$$

Combine $-4n$ and $-n$ to get $-5n$.

$$10m-5n$$

Expand

$10m-5n$

Solution Steps

Use the distributive property to multiply $\frac{1}{2}$ by $4m-8n$.

$$\frac{1}{2}\times 4m+\frac{1}{2}\left(-8\right)n+4\left(2m-\frac{1}{4}n\right)$$

Multiply $\frac{1}{2}$ and $4$ to get $\frac{4}{2}$.

$$\frac{4}{2}m+\frac{1}{2}\left(-8\right)n+4\left(2m-\frac{1}{4}n\right)$$

Divide $4$ by $2$ to get $2$.

$$2m+\frac{1}{2}\left(-8\right)n+4\left(2m-\frac{1}{4}n\right)$$

Multiply $\frac{1}{2}$ and $-8$ to get $\frac{-8}{2}$.

$$2m+\frac{-8}{2}n+4\left(2m-\frac{1}{4}n\right)$$

Divide $-8$ by $2$ to get $-4$.

$$2m-4n+4\left(2m-\frac{1}{4}n\right)$$

Use the distributive property to multiply $4$ by $2m-\frac{1}{4}n$.

$$2m-4n+8m+4\left(-\frac{1}{4}\right)n$$

Cancel out $4$ and $4$.

$$2m-4n+8m-n$$

Combine $2m$ and $8m$ to get $10m$.

$$10m-4n-n$$

Combine $-4n$ and $-n$ to get $-5n$.

$$10m-5n$$