Chapter 8.2, Problem 14GP

To determine

The solution of the equation $23-2c=41$ , and check the solution.

Answer to Problem 14GP

  $c=-9$

Explanation of Solution

Given:

The equation, $23-2c=41$ .

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 $23-2c=41$ for the unknown variable, isolate the variable term c on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate c on left side, first subtract 23 from both sides and then divide both sides by -2 and then simplify further as shown below,

  $\begin{array}{l}23-2c=41\\ 23-23-2c=41-23\\ -2c=18\\ \frac{-2c}{-2}=\frac{18}{-2}\\ c=-9\end{array}$

Thus, the solution of the given equation is $c=-9$ .

Now, to check the solution, substitute $c=-9$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}23-2c=41\\ 23-2\left(-9\right)=41\\ 23+18=41\\ 41=41\text{True Statement}\end{array}$

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