Let's break down the question and the steps required to solve it.
Shana wants to use all 62 feet of fencing to make a rectangular dog run with a specified length of 20 feet. She writes the equation [tex]\(21 + 2w = 62\)[/tex] to find the width [tex]\(w\)[/tex].
1. Simplify the Equation:
[tex]\[
21 + 2w = 62
\][/tex]
2. Isolate the term containing the variable [tex]\(w\)[/tex]:
We need to move the constant term (21) from the left side of the equation:
[tex]\[
2w = 62 - 21
\][/tex]
[tex]\[
2w = 41
\][/tex]
3. Solve for [tex]\(w\)[/tex]:
To isolate [tex]\(w\)[/tex], divide both sides of the equation by 2:
[tex]\[
w = \frac{41}{2}
\][/tex]
[tex]\[
w = 20.5
\][/tex]
Now, let's discuss the provided statements to determine which ones are true:
The value of [tex]\(w\)[/tex] is 10 feet:
- False. The value of [tex]\(w\)[/tex] is 20.5 feet.
The value of [tex]\(w\)[/tex] can be zero:
- False. Since [tex]\(w\)[/tex] is found to be 20.5, it cannot be zero in this problem’s context.
The value of [tex]\(w\)[/tex] cannot be a negative number:
- True. Since [tex]\(w\)[/tex] is a width measurement in a real-world context, it cannot logically be negative. The value we found (20.5) is a positive number.
Substitution is used to replace the variable [tex]\(l\)[/tex] with a value of 20:
- False. There is no substitution involving [tex]\(l\)[/tex] in the given equation. We simply solved for [tex]\(w\)[/tex].
* The subtraction property of equality is used to isolate the term with the variable [tex]\(w\)[/tex]:
- True. We subtracted 21 from both sides to isolate the term with [tex]\(w\)[/tex].
So, summarizing the true statements:
- The value of [tex]\(w\)[/tex] cannot be a negative number - True.
- The subtraction property of equality is used to isolate the term with the variable [tex]\(w\)[/tex] - True.
Therefore, these statements are the accurate reflections of the solution process.
