Chapter 1.8, Problem 65PPE

To determine

The solution of the equation $18-\left(-f\right)=91$ , and check the solution.

Answer to Problem 65PPE

  $f=73$

Explanation of Solution

Given:

The equation, $18-\left(-f\right)=91$ .

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 $18-\left(-f\right)=91$ for the unknown variable, isolate the variable term f on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate f on left side, first distribute the negative sign inside the parenthesis and then subtract 18 from both sides to simplify further as shown below,

  $\begin{array}{c}18-\left(-f\right)=91\\ 18+f=91\\ 18+f-18=91-18\\ f=73\end{array}$

Thus, the solution of the given equation is $f=73$ .

Now, to check the solution, substitute $f=73$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{c}18-\left(-f\right)=91\\ 18-\left(-73\right)=91\\ 18+73=91\\ 91=91\text{True Statement}\end{array}$

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