Solve 10*7/8[10(x-5)+x]=4n-61/4

$$10 \cdot \frac { 7 } { 8 } [ 10 ( x - 5 ) + x ] = 4 n - 6 \frac { 1 } { 4 }$$

Solve for n

$$n=\frac{385x-1725}{16}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 8,4.

$$80\times \frac{7}{8}\left(10\left(x-5\right)+x\right)=32n-2\left(6\times 4+1\right)$$

Multiply 80 and \frac{7}{8} to get 70.

$$70\left(10\left(x-5\right)+x\right)=32n-2\left(6\times 4+1\right)$$

Use the distributive property to multiply 10 by x-5.

$$70\left(10x-50+x\right)=32n-2\left(6\times 4+1\right)$$

Combine 10x and x to get 11x.

$$70\left(11x-50\right)=32n-2\left(6\times 4+1\right)$$

Use the distributive property to multiply 70 by 11x-50.

$$770x-3500=32n-2\left(6\times 4+1\right)$$

Multiply 6 and 4 to get 24.

$$770x-3500=32n-2\left(24+1\right)$$

Add 24 and 1 to get 25.

$$770x-3500=32n-2\times 25$$

Multiply -2 and 25 to get -50.

$$770x-3500=32n-50$$

Swap sides so that all variable terms are on the left hand side.

$$32n-50=770x-3500$$

Add 50 to both sides.

$$32n=770x-3500+50$$

Add -3500 and 50 to get -3450.

$$32n=770x-3450$$

Divide both sides by 32.

$$\frac{32n}{32}=\frac{770x-3450}{32}$$

Dividing by 32 undoes the multiplication by 32.

$$n=\frac{770x-3450}{32}$$

Divide 770x-3450 by 32.

$$n=\frac{385x-1725}{16}$$

Solve for x

$$x=\frac{16n}{385}+\frac{345}{77}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 8,4.

$$80\times \frac{7}{8}\left(10\left(x-5\right)+x\right)=32n-2\left(6\times 4+1\right)$$

Multiply 80 and \frac{7}{8} to get 70.

$$70\left(10\left(x-5\right)+x\right)=32n-2\left(6\times 4+1\right)$$

Use the distributive property to multiply 10 by x-5.

$$70\left(10x-50+x\right)=32n-2\left(6\times 4+1\right)$$

Combine 10x and x to get 11x.

$$70\left(11x-50\right)=32n-2\left(6\times 4+1\right)$$

Use the distributive property to multiply 70 by 11x-50.

$$770x-3500=32n-2\left(6\times 4+1\right)$$

Multiply 6 and 4 to get 24.

$$770x-3500=32n-2\left(24+1\right)$$

Add 24 and 1 to get 25.

$$770x-3500=32n-2\times 25$$

Multiply -2 and 25 to get -50.

$$770x-3500=32n-50$$

Add 3500 to both sides.

$$770x=32n-50+3500$$

Add -50 and 3500 to get 3450.

$$770x=32n+3450$$

Divide both sides by 770.

$$\frac{770x}{770}=\frac{32n+3450}{770}$$

Dividing by 770 undoes the multiplication by 770.

$$x=\frac{32n+3450}{770}$$

Divide 32n+3450 by 770.

$$x=\frac{16n}{385}+\frac{345}{77}$$