Chapter 8.5, Problem 3GP

To determine

The solution of the equation $1.4z-6=2.9z+9$ ,

Answer to Problem 3GP

  $z=-10$

Explanation of Solution

Given:

The equation, $1.4z-6=2.9z+9$

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 $1.4z-6=2.9z+9$ 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 subtract both sides by $2.9z$ and then add both sides by $6$ and then divide both sides by $-1.5$ and then simplify further as shown below,

  $\begin{array}{c}1.4z-6=2.9z+9\\ 1.4z-6-2.9z=2.9z+9-2.9z\\ -1.5z-6=9\\ -1.5z-6+6=9+6\\ -1.5z=15\\ \frac{-1.5z}{-1.5}=\frac{15}{-1.5}\\ z=-10\end{array}$

Thus, the solution of the given equation is $z=-10$ .