Chapter 8.2, Problem 30IP

To determine

The solution of the equation $25=2c-9$ , and check the solution.

Answer to Problem 30IP

  $c=17$

Explanation of Solution

Given:

The equation, $25=2c-9$ .

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 $25=2c-9$ 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 right side, first add 9 both sides and then divide both sides by 2 and then simplify further as shown below,

  $\begin{array}{l}25=2c-9\\ 25+9=2c-9+9\\ 34=2c\\ \frac{34}{2}=\frac{2c}{2}\\ 17=c\end{array}$

Thus, the solution of the given equation is $c=17$ .

Now, to check the solution, substitute $c=17$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}25=2c-9\\ 25=2\left(17\right)-9\\ 25=34-9\\ 25=25\text{True Statement}\end{array}$

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