Chapter 8.5, Problem 2GP

To determine

The solution of the equation $4y=2y-10$ ,

Answer to Problem 2GP

  $y=-5$

Explanation of Solution

Given:

The equation, $4y=2y-10$

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 $4y=2y-10$ 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 $2y$ and then divide both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}4y=2y-10\\ 4y-2y=2y-10-2y\\ 2y=-10\\ \frac{2y}{2}=\frac{-10}{2}\\ y=-5\end{array}$

Thus, the solution of the given equation is $y=-5$ .