Chapter 10, Problem 24SGR

To determine

The equation $y=\frac{2x+2}{3}$ for x .

Answer to Problem 24SGR

  $x=\frac{3y-2}{2}$

Explanation of Solution

Given information:

The equation is: $y=\frac{2x+2}{3}$ .

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.

Calculationy:

In order to solve the formula for x , first multiply both sides by 3 , then subtract 2 from both sides and then divide both sides by 2, to simplify further as shown below:

  $\begin{array}{l}y=\frac{2x+2}{3}\\ 3\times y=3\times \frac{2x+2}{3}\\ 3y=2x+2\\ 3y-2=2x+2-2\\ 3y-2=2x\\ \frac{3y-2}{2}=\frac{2x}{2}\\ x=\frac{3y-2}{2}\end{array}$

Thus, the formula is $x=\frac{3y-2}{2}$ .