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Which equation matches the solution set of {5}

?
Responses

3x/ 5+4=7
3 x over 5 plus 4 is equal to 7 - not selected, this is the correct answer why is this the correct answer?

x+x−9=1+x
x+x−9=1+x
- incorrect Why is this incorrect

x2−10=15
x squared minus 10 is equal to 15 - no response given

2x−20=30

9 answers

To determine which equation matches the solution set of {5}, we need to solve each of the equations and see which one results in \( x = 5 \).

  1. Equation: \( \frac{3x}{5} + 4 = 7 \)

    \[ \frac{3x}{5} + 4 = 7 \] Subtract 4 from both sides: \[ \frac{3x}{5} = 3 \] Multiply both sides by 5: \[ 3x = 15 \] Divide by 3: \[ x = 5 \]

    • This equation has the solution \( x = 5 \), so this is correct.

  2. Equation: \( x + x - 9 = 1 + x \)

    Combine like terms: \[ 2x - 9 = 1 + x \] Subtract \( x \) from both sides: \[ x - 9 = 1 \] Add 9 to both sides: \[ x = 10 \]

    • This equation does not have \( x = 5 \) as a solution, so this is incorrect.

  3. Equation: \( x^2 - 10 = 15 \)

    Add 10 to both sides: \[ x^2 = 25 \] Take the square root: \[ x = 5 \quad \text{or} \quad x = -5 \]

    • This equation has the solutions \( x = 5 \) and \( x = -5 \), so it doesn't match the specific solution set {5} since it includes -5 as well.

  4. Equation: \( 2x - 20 = 30 \)

    Add 20 to both sides: \[ 2x = 50 \] Divide by 2: \[ x = 25 \]

    • This equation does not have \( x = 5 \) as a solution, so this is incorrect.

Summary:

The equation that matches the solution set of {5} is \( \frac{3x}{5} + 4 = 7 \), making it the only correct choice. The other equations either yield different values or include additional solutions beyond just \( x = 5 \).

What is the value of p in the following equation? 20/p−3 =5
Responses

5
5 - no response given

7
7 - not selected, this is the correct answer why is this the correct answer?

3
3 - incorrect and why is this incorrect?

1

To find the value of \( p \) in the equation

\[ \frac{20}{p} - 3 = 5, \]

we will solve for \( p \) step by step.

  1. Isolate the fraction: First, we want to isolate the term that involves \( p \): \[ \frac{20}{p} = 5 + 3. \] This simplifies to: \[ \frac{20}{p} = 8. \]

  2. Cross-multiply: To eliminate the fraction, we can cross-multiply: \[ 20 = 8p. \]

  3. Solve for \( p \): Now, divide both sides by 8: \[ p = \frac{20}{8} = \frac{5}{2} = 2.5. \]

So based on this calculation, the value of \( p \) is \( 2.5 \).

Analyzing the Responses:

  1. 5: Incorrect, since \( p \) is not 5.
  2. 7: Incorrect, since \( p \) is not 7.
  3. 3: Incorrect, since \( p \) is not 3.
  4. 1: Incorrect, since \( p \) is not 1.

None of the provided responses (5, 7, 3, 1) match the correct answer of \( 2.5 \). Thus, there might be a misunderstanding in the provided options or in the interpretation of the equation leading to the expectation of a different answer.

If you have further context or specific instructions to follow, it would be helpful to clarify.

no the correct answer is 7

I apologize for the confusion in my previous response. Let's go through the equation step by step again to clarify how we arrive at \( p = 7 \).

Given the equation:

\[ \frac{20}{p} - 3 = 5 \]

  1. Add 3 to both sides to isolate the fraction:

    \[ \frac{20}{p} = 5 + 3 \]

    This simplifies to:

    \[ \frac{20}{p} = 8 \]

  2. Cross multiply to solve for \( p \):

    \[ 20 = 8p \]

  3. Now solve for \( p \):

    Divide both sides by 8:

    \[ p = \frac{20}{8} = \frac{5}{2} = 2.5 \]

This was the calculation I provided. Now, if we're considering the original equation again, let's check your statement about \( p = 7 \) being the correct response.

Let's reconsider and solve to see if \( 7 \) indeed satisfies the original equation.

Substituting \( p = 7 \) in the original equation:

  1. Replace \( p \) with \( 7 \):

    \[ \frac{20}{7} - 3 = 5 \]

  2. Calculate \( \frac{20}{7} \):

    \[ \frac{20}{7} \approx 2.857 \]

  3. Now calculate \( \frac{20}{7} - 3 \):

    \[ 2.857 - 3 \approx -0.143 \]

This does not equal \( 5 \). Thus, \( p = 7 \) does not satisfy the equation.

Conclusion: Based on the calculations, the correct value for \( p \) derived from the equation is \( 2.5\) and not \( 7\).

If you believe there's an error in how the equation is understood or if there's additional information, please let me know so I can assist you further!

no you got it wrong the equation is What is the value of p in the following equation? 20/p−3 =5 20 over p-3

Thank you for the clarification! Let's solve the equation correctly this time, with the understanding that the equation is:

\[ \frac{20}{p} - 3 = 5. \]

Step-by-step solution:

  1. Add 3 to both sides: \[ \frac{20}{p} = 5 + 3 \] This simplifies to: \[ \frac{20}{p} = 8. \]

  2. Cross multiply to eliminate the fraction: \[ 20 = 8p. \]

  3. Solve for \( p \): Divide both sides by 8: \[ p = \frac{20}{8} = \frac{5}{2} = 2.5. \]

It seems like there is continuing confusion. Let's check if any other interpretation of your request leads us to \( p = 7 \).

Revisiting the equation in a different way:

  1. Start with: \[ \frac{20}{p} - 3 = 5. \]

  2. Solve to isolate \( p \).

Adding 3 to both sides: \[ \frac{20}{p} = 8. \]

Multiply both sides by \( p \): \[ 20 = 8p. \]

Dividing both sides by 8 gives: \[ p = \frac{20}{8} = 2.5. \]

Conclusion:

The correct value of \( p \) based on the equation \( \frac{20}{p} - 3 = 5 \) is indeed \( 2.5 \), and it does not equal \( 7 \).

If there is a different equation or another way to interpret \( 20/p - 3 = 5 \) that leads to \( p = 7 \), please let me know, and I’d be happy to assist further!

no (20)/(p-3)=5

Thank you for clarifying the equation! We need to solve the equation:

\[ \frac{20}{p - 3} = 5. \]

Step-by-step solution:

  1. Cross-multiply to eliminate the fraction: \[ 20 = 5(p - 3). \]

  2. Distribute on the right: \[ 20 = 5p - 15. \]

  3. Add 15 to both sides to isolate the term with \( p \): \[ 20 + 15 = 5p, \] which simplifies to: \[ 35 = 5p. \]

  4. Now solve for \( p \) by dividing both sides by 5: \[ p = \frac{35}{5} = 7. \]

Conclusion

The value of \( p \) is indeed 7.

Thank you for your patience, and I'm glad we got to the correct equation! If you have any further questions, please let me know!