Question 1: Which equation matches the solution set of {5}?
To determine which equation has the solution set of {5}, we can solve each equation for \(x\) and see which one results in \(x = 5\).
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\(x + x - 9 = 1 + x\) \[ 2x - 9 = 1 + x \ 2x - x = 1 + 9 \ x = 10 , \text{(not a match)} \]
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\(2x - 20 = 30\) \[ 2x = 30 + 20 \ 2x = 50 \ x = 25 , \text{(not a match)} \]
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\(x^2 - 10 = 15\) \[ x^2 = 15 + 10 \ x^2 = 25 \ x = 5 , \text{or} , x = -5 , \text{(partial match)} \]
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\(3x + 4 = 7\) (Note: it seems there may be a typo in how this is presented; it may mean \(3x + 4 = 7\)) \[ 3x = 7 - 4 \ 3x = 3 \ x = 1 , \text{(not a match)} \]
The equation that matches the solution set {5} is:
\(x^2 - 10 = 15\) (since it has a solution of \(x = 5\)).
Question 2: What is the value of \(p\) in the following equation?
Given:
\(20p - 3 = 5\)
To solve for \(p\): \[ 20p = 5 + 3 \ 20p = 8 \ p = \frac{8}{20} \ p = \frac{2}{5} \approx 0.4 , \text{(not an option)} \]
In the given options: 1, 3, 5, 7, none match our result. Please check if the equation provided is correct.
Question 3: Which of the following equations has the solution set \(x = {-95, 3}\)?
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\((x - 3)(9x + 5) = 0\)
- Solutions: \(x = 3\) and \(9x + 5 = 0\) gives \(x = -\frac{5}{9}\) (not a match).
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\(-3x(5x + 9) = 0\)
- Solutions: \(x = 0\) and \(5x + 9 = 0\) gives \(x = -\frac{9}{5}\) (not a match).
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\((x + 3)(9x - 5) = 0\)
- Solutions: \(x = -3\) and \(9x - 5 = 0\) gives \(x = \frac{5}{9}\) (not a match).
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\((x - 3)(5x + 9) = 0\)
- Solutions: \(x = 3\) and \(5x + 9 = 0\) gives \(x = -\frac{9}{5}\) (not a match).
None of the above equations directly represent the solution set \(x = {-95, 3}\). The equation that should represent this condition is: \[ (x - 3)(x + 95) = 0 \]
This indicates that there may be an oversight in the provided options. Please recheck the equations again for correctness.
2 answers