Solve sqrt{47-3x/2}=4

$$\sqrt { \frac { 47 - 3 x } { 2 } } = 4$$

Solve for x

$$x=5$$

Steps for Solving Radical Equations

Divide each term of 47-3x by 2 to get \frac{47}{2}-\frac{3}{2}x.

$$\sqrt{\frac{47}{2}-\frac{3}{2}x}=4$$

Square both sides of the equation.

$$-\frac{3}{2}x+\frac{47}{2}=16$$

Subtract \frac{47}{2} from both sides of the equation.

$$-\frac{3}{2}x+\frac{47}{2}-\frac{47}{2}=16-\frac{47}{2}$$

Subtracting \frac{47}{2} from itself leaves 0.

$$-\frac{3}{2}x=16-\frac{47}{2}$$

Subtract \frac{47}{2} from 16.

$$-\frac{3}{2}x=-\frac{15}{2}$$

Divide both sides of the equation by -\frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{2}x}{-\frac{3}{2}}=-\frac{\frac{15}{2}}{-\frac{3}{2}}$$

Dividing by -\frac{3}{2} undoes the multiplication by -\frac{3}{2}.

$$x=-\frac{\frac{15}{2}}{-\frac{3}{2}}$$

Divide -\frac{15}{2} by -\frac{3}{2} by multiplying -\frac{15}{2} by the reciprocal of -\frac{3}{2}.

$$x=5$$