Chapter 1.8, Problem 54PPE

To determine

The solution of the equation $12=\frac{x}{-3}$ , and check the solution.

Answer to Problem 54PPE

  $x=-36$

Explanation of Solution

Given:

The equation, $12=\frac{x}{-3}$ .

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.

Calculation:

In order to solve the given equation $12=\frac{x}{-3}$ for the unknown variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on right side, first multiply both sides by the $-3$ to get rid of the denominator on the right side and then simplify further as shown below,

  $\begin{array}{c}12=\frac{x}{-3}\\ 12\cdot \left(-3\right)=\frac{x}{-3}\cdot \left(-3\right)\\ -36=x\end{array}$

Thus, the solution of the given equation is $x=-36$ .

Now, to check the solution, substitute $x=-36$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{c}12=\frac{x}{-3}\\ 12=\frac{-36}{-3}\\ 12=12\text{True Statement}\end{array}$

Since, the left hand side and right hand side are equal, so the solution is correct.