Solve n1/2(7x-2)+6x=37

$$n \frac { 1 } { 2 } ( 7 x - 2 ) + 6 x = 37$$

Solve for n

$$n=-\frac{2\left(6x-37\right)}{7x-2}$$

$$x\neq \frac{2}{7}$$

Steps for Solving Linear Equation

Use the distributive property to multiply n\times \frac{1}{2} by 7x-2.

$$\frac{7}{2}nx-2n\times \frac{1}{2}+6x=37$$

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

$$\frac{7}{2}nx-n+6x=37$$

Subtract 6x from both sides.

$$\frac{7}{2}nx-n=37-6x$$

Combine all terms containing n.

$$\left(\frac{7}{2}x-1\right)n=37-6x$$

The equation is in standard form.

$$\left(\frac{7x}{2}-1\right)n=37-6x$$

Divide both sides by \frac{7}{2}x-1.

$$\frac{\left(\frac{7x}{2}-1\right)n}{\frac{7x}{2}-1}=\frac{37-6x}{\frac{7x}{2}-1}$$

Dividing by \frac{7}{2}x-1 undoes the multiplication by \frac{7}{2}x-1.

$$n=\frac{37-6x}{\frac{7x}{2}-1}$$

Divide 37-6x by \frac{7}{2}x-1.

$$n=\frac{2\left(37-6x\right)}{7x-2}$$

Solve for x

$$x=\frac{2\left(n+37\right)}{7n+12}$$

$$n\neq -\frac{12}{7}$$

Steps for Solving Linear Equation

Use the distributive property to multiply n\times \frac{1}{2} by 7x-2.

$$\frac{7}{2}xn-2n\times \frac{1}{2}+6x=37$$

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

$$\frac{7}{2}xn-n+6x=37$$

Add n to both sides.

$$\frac{7}{2}xn+6x=37+n$$

Combine all terms containing x.

$$\left(\frac{7}{2}n+6\right)x=37+n$$

The equation is in standard form.

$$\left(\frac{7n}{2}+6\right)x=n+37$$

Divide both sides by \frac{7}{2}n+6.

$$\frac{\left(\frac{7n}{2}+6\right)x}{\frac{7n}{2}+6}=\frac{n+37}{\frac{7n}{2}+6}$$

Dividing by \frac{7}{2}n+6 undoes the multiplication by \frac{7}{2}n+6.

$$x=\frac{n+37}{\frac{7n}{2}+6}$$

Divide n+37 by \frac{7}{2}n+6.

$$x=\frac{2\left(n+37\right)}{7n+12}$$