Solve 1/4sqrt{7/9x-1/3}=sqrt{4/9}-frac{1}{6}

$$\frac{ 1 }{ 4 } \sqrt{ \frac{ 7 }{ 9 } x- \frac{ 1 }{ 3 } } = \sqrt{ \frac{ 4 }{ 9 } } - \frac{ 1 }{ 6 }$$

Solve for x

$$x = \frac{39}{7} = 5\frac{4}{7} \approx 5.571428571$$

Steps for Solving Radical Equations

Multiply both sides by 4.

$$\frac{\frac{1}{4}\sqrt{\frac{7}{9}x-\frac{1}{3}}}{\frac{1}{4}}=\frac{\frac{1}{2}}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$\sqrt{\frac{7}{9}x-\frac{1}{3}}=\frac{\frac{1}{2}}{\frac{1}{4}}$$

Divide \frac{1}{2} by \frac{1}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{4}.

$$\sqrt{\frac{7}{9}x-\frac{1}{3}}=2$$

Square both sides of the equation.

$$\frac{7}{9}x-\frac{1}{3}=4$$

Add \frac{1}{3} to both sides of the equation.

$$\frac{7}{9}x-\frac{1}{3}-\left(-\frac{1}{3}\right)=4-\left(-\frac{1}{3}\right)$$

Subtracting -\frac{1}{3} from itself leaves 0.

$$\frac{7}{9}x=4-\left(-\frac{1}{3}\right)$$

Subtract -\frac{1}{3} from 4.

$$\frac{7}{9}x=\frac{13}{3}$$

Divide both sides of the equation by \frac{7}{9}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{7}{9}x}{\frac{7}{9}}=\frac{\frac{13}{3}}{\frac{7}{9}}$$

Dividing by \frac{7}{9} undoes the multiplication by \frac{7}{9}.

$$x=\frac{\frac{13}{3}}{\frac{7}{9}}$$

Divide \frac{13}{3} by \frac{7}{9} by multiplying \frac{13}{3} by the reciprocal of \frac{7}{9}.

$$x=\frac{39}{7}$$