Chapter 8.2, Problem 44IP

To determine

The solution of the equation $46-3n=-23$ , and check the solution.

Answer to Problem 44IP

  $n=23$

Explanation of Solution

Given:

The equation, $46-3n=-23$ .

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 $46-3n=-23$ for the unknown variable, isolate the variable term n on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate n on left side, firstsubtract 46 from both sides and then divide both sides by -3 to simplify further as shown below,

  $\begin{array}{l}46-3n=-23\\ 46-46-3n=-23-46\\ -3n=-69\\ \frac{-3n}{-3}=\frac{-69}{-3}\\ n=23\end{array}$

Thus, the solution of the given equation is $n=23$ .

Now, to check the solution, substitute $x=-11$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}46-3n=-23\\ 46-3\left(23\right)=-23\\ 46-69=-23\\ -23=-23\text{True Statement}\end{array}$

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