Chapter 8.4, Problem 37IP

To determine

The solution of the equation $4.1(m+4)-2.1m=6$ .

Answer to Problem 37IP

  $m=-5.2$

Explanation of Solution

Given:

The equation, $4.1(m+4)-2.1m=6$ .

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 $4.1(m+4)-2.1m=6$ for the unknown variable, first multiplying 4.1 inside the bracket then combine the terms which have variable in left side , now the equation is as shown below:

  $\begin{array}{l}4.1(m+4)-2.1m=6\\ 4.1m+16.4-2.1m=6\\ 2m+16.4=6\end{array}$

Here to isolate m on left side, first subtract 16.4 from both sides and then divide both sides by 2 and then simplify further as shown below,

  $\begin{array}{l}2m+16.4=6\\ 2m+16.4-16.4=6-16.4\\ 2m=-10.4\\ \frac{2m}{2}=\frac{-10.4}{2}\\ m=-5.2\end{array}$

Thus, the solution of the given equation is $m=-5.2$ .