Solve 7-2/3sqrt{1-x}=3

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

Solve for x

$$x=-35$$

Steps for Solving Radical Equations

Subtract 7 from both sides of the equation.

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

Subtracting 7 from itself leaves 0.

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

Subtract 7 from 3.

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

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

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

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

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

Divide -4 by -\frac{2}{3} by multiplying -4 by the reciprocal of -\frac{2}{3}.

$$\sqrt{-x+1}=6$$

Square both sides of the equation.

$$-x+1=36$$

Subtract 1 from both sides of the equation.

$$-x+1-1=36-1$$

Subtracting 1 from itself leaves 0.

$$-x=36-1$$

Subtract 1 from 36.

$$-x=35$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{35}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{35}{-1}$$

Divide 35 by -1.

$$x=-35$$