Solve |3-y+1|/sqrt{1+1}=3

$$\frac { | 3 - y + 1 | } { \sqrt { 1 + 1 } } = 3$$

Solve for y

$$y=3\sqrt{2}+4\approx 8.242640687$$

$$y=4-3\sqrt{2}\approx -0.242640687$$

Steps Using Definition of Absolute Value

Add 3 and 1 to get 4.

$$\frac{|4-y|}{\sqrt{1+1}}=3$$

Add 1 and 1 to get 2.

$$\frac{|4-y|}{\sqrt{2}}=3$$

Rationalize the denominator of \frac{|4-y|}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{|4-y|\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=3$$

The square of \sqrt{2} is 2.

$$\frac{|4-y|\sqrt{2}}{2}=3$$

Multiply both sides by 2.

$$|4-y|\sqrt{2}=3\times 2$$

Multiply 3 and 2 to get 6.

$$|4-y|\sqrt{2}=6$$

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. Remember to follow the order of operations.

$$\sqrt{2}|-y+4|=6$$

Divide both sides by \sqrt{2}.

$$|-y+4|=3\sqrt{2}$$

Use the definition of absolute value.

$$-y+4=3\sqrt{2} -y+4=-3\sqrt{2}$$

Subtract 4 from both sides of the equation.

$$-y=3\sqrt{2}-4 -y=-3\sqrt{2}-4$$

Divide both sides by -1.

$$y=4-3\sqrt{2} y=3\sqrt{2}+4$$