Read the word problem. Look at the student's work and solution.Henry and Rick have 265.3 downloaded minutes of music. If Henry has 112 minutes, how many minutes belong to Rick?

Question

112 + r = 265.3
-112 +112
----------------
r = 377.3

Part A: Identify the error in the student's work and describe it.

Part B: Solve the problem correctly. How many minutes belong to Rick?

Answer 1

Part A: Identify the error in the student's work and describe it.

The student's equation is set up correctly as \(112 + r = 265.3\). However, the mistake occurs in the subtraction step where they incorrectly calculated \(r\). Instead of subtracting 112 from both sides and calculating \(r\) as \(r = 265.3 - 112\), the student erroneously added 112 to 265.3, resulting in \(r = 377.3\).

Part B: Solve the problem correctly. How many minutes belong to Rick?

To find the number of minutes belonging to Rick, we start with the correct equation:

\[ 112 + r = 265.3 \]

Now, to isolate \(r\), we'll subtract 112 from both sides:

\[ r = 265.3 - 112 \]

Now, we perform the subtraction:

\[ r = 153.3 \]

Thus, Rick has 153.3 minutes of downloaded music.

Answer 2

select the operation that should be done to both sides of the equation to solve for the value of x.(4 points)

x + 15 = -23

x15 = 7

-5x = 40

x - 23 = 49

Answer 3

To solve for \( x \) in each equation, we need to identify the appropriate operation to be performed on both sides of the equation. Here’s how to solve each equation:

1. For the equation: \[ x + 15 = -23 \] Operation: Subtract 15 from both sides. \[ x + 15 - 15 = -23 - 15 \implies x = -38 \]

2. For the equation: \[ x \cdot 15 = 7 \] Operation: Divide both sides by 15. \[ \frac{x \cdot 15}{15} = \frac{7}{15} \implies x = \frac{7}{15} \]

3. For the equation: \[ -5x = 40 \] Operation: Divide both sides by -5. \[ \frac{-5x}{-5} = \frac{40}{-5} \implies x = -8 \]

4. For the equation: \[ x - 23 = 49 \] Operation: Add 23 to both sides. \[ x - 23 + 23 = 49 + 23 \implies x = 72 \]

In summary, the operations to perform on both sides for each equation are:

1. Subtract 15 from both sides.
2. Divide both sides by 15.
3. Divide both sides by -5.
4. Add 23 to both sides.

Answer 4

select the operation that should be done to both sides of the equation to solve for the value of x.(4 points)
x + 15 = -23

x/15 = 7

-x5= 40

x - 23 = 49

Answer 5

Here are the operations that should be done to both sides of the equations to solve for the value of \( x \):

1. For the equation: \[ x + 15 = -23 \] Operation: Subtract 15 from both sides. \[ x + 15 - 15 = -23 - 15 \implies x = -38 \]

2. For the equation: \[ \frac{x}{15} = 7 \] Operation: Multiply both sides by 15. \[ 15 \cdot \frac{x}{15} = 15 \cdot 7 \implies x = 105 \]

3. For the equation: \[ -5x = 40 \] Operation: Divide both sides by -5. \[ \frac{-5x}{-5} = \frac{40}{-5} \implies x = -8 \]

4. For the equation: \[ x - 23 = 49 \] Operation: Add 23 to both sides. \[ x - 23 + 23 = 49 + 23 \implies x = 72 \]

To summarize:

1. Subtract 15 from both sides for \( x + 15 = -23 \).
2. Multiply both sides by 15 for \( \frac{x}{15} = 7 \).
3. Divide both sides by -5 for \( -5x = 40 \).
4. Add 23 to both sides for \( x - 23 = 49 \).