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Anita has soccer practice every day after school. On Friday, practice is only 1 hour. If she practices a total of 9 hours, how long is practice on each of the other 4 days?



Write and solve an equation to answer the question, and then identify which statement is not true.


AThe equation is $4 x+1=9$.
B$x$ represents the practice time on Monday, Tuesday, Wednesday, and Thursday.
CThe solution is $x=3$.
DThe first step in solving the equation is to subtract 1 from both sides of the equation.

Verified Answer :

  • The equation representing the practice time is \(4x + 1 = 9\), where \(x\) is the time spent on each of the first 4 days.
  • Solving the equation, subtract 1 from both sides to get \(4x = 8\), then divide by 4 to get \(x = 2\).
  • Comparing this with the given statements, "The solution is \(x = 3\)" is clearly incorrect because the calculated value is \(2\).
  • The false statement is \(\boxed{\text{The solution is } x = 3}\).

Explanation

  1. Analyzing the Problem and Setting Up the Equation

Anita practices soccer for five days total: Monday, Tuesday, Wednesday, Thursday, and Friday. We are given that Friday's practice lasts for \(1\) hour and the total duration for all five days is \(9\) hours. Let \(x\) represent the number of hours she spends at practice on each of the other four days. Since each of these four days has the same duration \(x\), the total time spent for these four days is \(4x\). Adding the \(1\) hour from Friday, we can express the total time as the sum \(4x + 1 = 9\).

  1. Solving the Equation

To find the value of \(x\), we solve the equation \(4x + 1 = 9\). First, we subtract \(1\) from both sides of the equation to isolate the term containing \(x\):
\[4x + 1 - 1 = 9 - 1\]
\[4x = 8\]
Next, we divide both sides by \(4\):
\[\frac{4x}{4} = \frac{8}{4}\]
\[x = 2\]
Thus, Anita spends \(2\) hours at practice on each of the four days.

  1. Identifying the False Statement

Now we evaluate the given statements based on our results:

  • "The equation is \(4x + 1 = 9\)": This is true as derived in step 1.
  • "\(x\) represents the practice time on Monday, Tuesday, Wednesday, and Thursday": This is true by our definition of \(x\).
  • "The solution is \(x = 3\)": This is false, as our calculation shows \(x = 2\).
  • "The first step in solving the equation is to subtract \(1\) from both sides of the equation": This is true, as demonstrated in step 2.

Therefore, the statement "The solution is \(x = 3\)" is the one that is not true.

Examples

Understanding how to set up and solve equations is essential for managing your daily schedule. For example, if you have a certain amount of time for homework each week and you know how much you spend on Friday, you can create an equation to determine how much time you should dedicate on the other school days to meet your total goal. This ensures you manage your time effectively and keep up with your responsibilities!

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