Solve n7/6(-x+4)=-2

$$n \frac { 7 } { 6 } ( - x + 4 ) = - 2$$

Solve for n

$$n=-\frac{12}{7\left(4-x\right)}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Use the distributive property to multiply n\times \frac{7}{6} by -x+4.

$$\frac{7}{6}n\left(-x\right)+4n\times \frac{7}{6}=-2$$

Multiply 4 and \frac{7}{6} to get \frac{14}{3}.

$$\frac{7}{6}n\left(-x\right)+\frac{14}{3}n=-2$$

Multiply \frac{7}{6} and -1 to get -\frac{7}{6}.

$$-\frac{7}{6}nx+\frac{14}{3}n=-2$$

Combine all terms containing n.

$$\left(-\frac{7}{6}x+\frac{14}{3}\right)n=-2$$

The equation is in standard form.

$$\left(-\frac{7x}{6}+\frac{14}{3}\right)n=-2$$

Divide both sides by -\frac{7}{6}x+\frac{14}{3}.

$$\frac{\left(-\frac{7x}{6}+\frac{14}{3}\right)n}{-\frac{7x}{6}+\frac{14}{3}}=-\frac{2}{-\frac{7x}{6}+\frac{14}{3}}$$

Dividing by -\frac{7}{6}x+\frac{14}{3} undoes the multiplication by -\frac{7}{6}x+\frac{14}{3}.

$$n=-\frac{2}{-\frac{7x}{6}+\frac{14}{3}}$$

Divide -2 by -\frac{7}{6}x+\frac{14}{3}.

$$n=-\frac{12}{7\left(4-x\right)}$$

Solve for x

$$x=4+\frac{12}{7n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply n\times \frac{7}{6} by -x+4.

$$\frac{7}{6}n\left(-x\right)+4n\times \frac{7}{6}=-2$$

Multiply 4 and \frac{7}{6} to get \frac{14}{3}.

$$\frac{7}{6}n\left(-x\right)+\frac{14}{3}n=-2$$

Subtract \frac{14}{3}n from both sides.

$$\frac{7}{6}n\left(-x\right)=-2-\frac{14}{3}n$$

Multiply \frac{7}{6} and -1 to get -\frac{7}{6}.

$$-\frac{7}{6}nx=-2-\frac{14}{3}n$$

The equation is in standard form.

$$\left(-\frac{7n}{6}\right)x=-\frac{14n}{3}-2$$

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

$$\frac{\left(-\frac{7n}{6}\right)x}{-\frac{7n}{6}}=\frac{-\frac{14n}{3}-2}{-\frac{7n}{6}}$$

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

$$x=\frac{-\frac{14n}{3}-2}{-\frac{7n}{6}}$$

Divide -2-\frac{14n}{3} by -\frac{7}{6}n.

$$x=4+\frac{12}{7n}$$