Solve D=9/7x-(2/3-2/7x)+5/3

$$D = \frac { 9 } { 7 } x - ( \frac { 2 } { 3 } - \frac { 2 } { 7 } x ) + \frac { 5 } { 3 }$$

Solve for D

$$D=\frac{11x}{7}+1$$

Solution Steps

To find the opposite of \frac{2}{3}-\frac{2}{7}x, find the opposite of each term.

$$D=\frac{9}{7}x-\frac{2}{3}+\frac{2}{7}x+\frac{5}{3}$$

Combine \frac{9}{7}x and \frac{2}{7}x to get \frac{11}{7}x.

$$D=\frac{11}{7}x-\frac{2}{3}+\frac{5}{3}$$

Add -\frac{2}{3} and \frac{5}{3} to get 1.

$$D=\frac{11}{7}x+1$$

Solve for x

$$x=\frac{7\left(D-1\right)}{11}$$

Steps for Solving Linear Equation

To find the opposite of \frac{2}{3}-\frac{2}{7}x, find the opposite of each term.

$$D=\frac{9}{7}x-\frac{2}{3}+\frac{2}{7}x+\frac{5}{3}$$

Combine \frac{9}{7}x and \frac{2}{7}x to get \frac{11}{7}x.

$$D=\frac{11}{7}x-\frac{2}{3}+\frac{5}{3}$$

Add -\frac{2}{3} and \frac{5}{3} to get 1.

$$D=\frac{11}{7}x+1$$

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

$$\frac{11}{7}x+1=D$$

Subtract 1 from both sides.

$$\frac{11}{7}x=D-1$$

Divide both sides of the equation by \frac{11}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{11}{7}x}{\frac{11}{7}}=\frac{D-1}{\frac{11}{7}}$$

Dividing by \frac{11}{7} undoes the multiplication by \frac{11}{7}.

$$x=\frac{D-1}{\frac{11}{7}}$$

Divide D-1 by \frac{11}{7} by multiplying D-1 by the reciprocal of \frac{11}{7}.

$$x=\frac{7D-7}{11}$$