Chapter 8.4, Problem 18IP

To determine

The solution of the equation $18=-3\left(m-6\right)$ .

Answer to Problem 18IP

  $m=0$

Explanation of Solution

Given:

The equation, $18=-3\left(m-6\right)$ .

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• 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 $18=-3\left(m-6\right)$ for the unknown variable, first using left Distributive property on right side of the equation and then isolate the variable term m on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate m on right side, first subtract 18 from both sides and then divide both sides by -3 and then simplify further as shown below,

  $\begin{array}{l}18=-3\left(m-6\right)\\ 18=-3\cdot m+\left(-3\right)\cdot \left(-6\right)\\ 18=-3m+18\\ 18-18=-3m+18-18\\ 0=-3m\\ \frac{0}{-3}=\frac{-3m}{-3}\\ 0=m\end{array}$

Thus, the solution of the given equation is $m=0$ .