Solve n5/2-3x-5+4x=-7/4

$$n \frac { 5 } { 2 } - 3 x - 5 + 4 x = - \frac { 7 } { 4 }$$

Solve for n

$$n=-\frac{2x}{5}+\frac{13}{10}$$

Steps for Solving Linear Equation

Combine -3x and 4x to get x.

$$n\times \frac{5}{2}+x-5=-\frac{7}{4}$$

Subtract x from both sides.

$$n\times \frac{5}{2}-5=-\frac{7}{4}-x$$

Add 5 to both sides.

$$n\times \frac{5}{2}=-\frac{7}{4}-x+5$$

Add -\frac{7}{4} and 5 to get \frac{13}{4}.

$$n\times \frac{5}{2}=\frac{13}{4}-x$$

The equation is in standard form.

$$\frac{5}{2}n=\frac{13}{4}-x$$

Divide both sides of the equation by \frac{5}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{2}n}{\frac{5}{2}}=\frac{\frac{13}{4}-x}{\frac{5}{2}}$$

Dividing by \frac{5}{2} undoes the multiplication by \frac{5}{2}.

$$n=\frac{\frac{13}{4}-x}{\frac{5}{2}}$$

Divide \frac{13}{4}-x by \frac{5}{2} by multiplying \frac{13}{4}-x by the reciprocal of \frac{5}{2}.

$$n=-\frac{2x}{5}+\frac{13}{10}$$

Solve for x

$$x=-\frac{5n}{2}+\frac{13}{4}$$

Solution Steps

Combine -3x and 4x to get x.

$$n\times \frac{5}{2}+x-5=-\frac{7}{4}$$

Subtract n\times \frac{5}{2} from both sides.

$$x-5=-\frac{7}{4}-n\times \frac{5}{2}$$

Add 5 to both sides.

$$x=-\frac{7}{4}-n\times \frac{5}{2}+5$$

Multiply -1 and \frac{5}{2} to get -\frac{5}{2}.

$$x=-\frac{7}{4}-\frac{5}{2}n+5$$

Add -\frac{7}{4} and 5 to get \frac{13}{4}.

$$x=\frac{13}{4}-\frac{5}{2}n$$