Solve |2-y|:(-2/5)=-113/32

$$| 2 - y | : ( - \frac { 2 } { 5 } ) = - 1 \frac { 13 } { 32 }$$

Solve for y

$$y = \frac{41}{16} = 2\frac{9}{16} = 2.5625$$

$$y = \frac{23}{16} = 1\frac{7}{16} = 1.4375$$

Steps Using Definition of Absolute Value

Multiply both sides of the equation by 32.

$$32\times \frac{|2-y|}{-\frac{2}{5}}=-\left(1\times 32+13\right)$$

Multiply 1 and 32 to get 32.

$$32\times \frac{|2-y|}{-\frac{2}{5}}=-\left(32+13\right)$$

Add 32 and 13 to get 45.

$$32\times \frac{|2-y|}{-\frac{2}{5}}=-45$$

Divide both sides by 32.

$$\frac{|2-y|}{-\frac{2}{5}}=-\frac{45}{32}$$

Multiply both sides by -\frac{2}{5}.

$$|2-y|=-\frac{45}{32}\left(-\frac{2}{5}\right)$$

Multiply -\frac{45}{32} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$|2-y|=\frac{-45\left(-2\right)}{32\times 5}$$

Do the multiplications in the fraction \frac{-45\left(-2\right)}{32\times 5}.

$$|2-y|=\frac{90}{160}$$

Reduce the fraction \frac{90}{160} to lowest terms by extracting and canceling out 10.

$$|2-y|=\frac{9}{16}$$

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.

$$|-y+2|=\frac{9}{16}$$

Use the definition of absolute value.

$$-y+2=\frac{9}{16} -y+2=-\frac{9}{16}$$

Subtract 2 from both sides of the equation.

$$-y=-\frac{23}{16} -y=-\frac{41}{16}$$

Divide both sides by -1.

$$y=\frac{23}{16} y=\frac{41}{16}$$