Chapter 8.3, Problem 34CCR

To determine

The solution of the equation $8z=14$

Answer to Problem 34CCR

  $z=\frac{7}{4}$

Explanation of Solution

Given:

The equation, $8z=14$

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 $8z=14$ for the variable, isolate the variable term z on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate z on left side, first divide both side by $8$ and then simplify further as shown below,

  $\begin{array}{c}8z=14\\ \frac{8z}{8}=\frac{14}{8}\\ z=\frac{7}{4}\end{array}$

Thus, the solution of the given equation is $z=\frac{7}{4}$ .