Chapter 8.2, Problem 76STP

To determine

The maximum distance m that she can run if her first training run is 3 miles

Answer to Problem 76STP

The solution of the given equation is $m=10$

Option A is correct

Explanation of Solution

Given:

The distance d that Maxie can run in her first training run is represented by the equation $d=\frac{1}{2}m-2$ and her first training run is $d=3miles$

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 $d=\frac{1}{2}m-2$ for the variable, isolate the variable term d on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate d on left side, first add both sides by $2$ and then multiply both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}d=\frac{1}{2}m-2\\ 3=\frac{1}{2}m-2\\ 3+2=\frac{1}{2}m-2+2\\ 5=\frac{1}{2}m\\ 5\times 2=\frac{1}{2}m\times 2\\ 10=m\\ \Rightarrow m=10\end{array}$

Thus, the solution of the given equation is $m=10$

Option A is correct