Chapter 8.2, Problem 59IP

To determine

The solution of the equation $\frac{2}{3}-6y=-1\frac{5}{6}$ ,

Answer to Problem 59IP

  $y=\frac{-5}{12}$

Explanation of Solution

Given:

The equation, $\frac{2}{3}-6y=-1\frac{5}{6}$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $\frac{2}{3}-6y=-1\frac{5}{6}$ for the variable, isolate the variable term y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate y on left side, first subtract both sides by $\frac{2}{3}$ and then divide both sides by $-6$ and then simplify further as shown below,

  $\begin{array}{c}\frac{2}{3}-6y=-1\frac{5}{6}\\ \frac{2}{3}-6y=-\frac{11}{6}\\ \frac{2}{3}-6y-\frac{2}{3}=-\frac{11}{6}-\frac{2}{3}\\ -6y=\frac{-11-4}{6}\\ -6y=\frac{-15}{6}\\ -6y=\frac{-5}{2}\\ \frac{-6y}{-6}=\frac{-5}{2\times 6}\\ y=\frac{-5}{12}\end{array}$

Thus, the solution of the given equation is $y=\frac{-5}{12}$ .