Let's tackle each question one by one.
Question 1
Which equation matches the solution set of {5}?
To find the equation that has a solution of x = 5, we can check each equation separately.
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\(x + x - 9 = 1 + x\)
- Simplifying: \[2x - 9 = 1 + x\] \[2x - x = 10\] \[x = 10\] (not a solution of {5})
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\(2x - 20 = 30\)
- Simplifying: \[2x = 30 + 20\] \[2x = 50\] \[x = 25\] (not a solution of {5})
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\(x^2 - 10 = 15\)
- Simplifying: \[x^2 = 15 + 10\] \[x^2 = 25\] \[x = 5 \text{ or } x = -5\] (has 5 as a solution)
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\(3x + 4 = 7\)
- Simplifying: \[3x = 7 - 4\] \[3x = 3\] \[x = 1\] (not a solution of {5})
The equation that matches the solution set {5} is \(x^2 - 10 = 15\).
Question 2
What is the value of p in the following equation? \( \frac{20}{p - 3} = 5 \)
We can solve for p:
\[ 20 = 5(p - 3) \] Expanding: \[ 20 = 5p - 15 \] Adding 15 to both sides: \[ 35 = 5p \] Dividing by 5: \[ p = 7 \]
The value of \( p \) is 7.
Question 3
Which of the following equations has the solution set \( x = {-\frac{9}{5}, 3} \)?
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\((x - 3)(9x + 5) = 0\)
- Roots are \( x - 3 = 0 \Rightarrow x = 3 \) and \( 9x + 5 = 0 \Rightarrow x = -\frac{5}{9} \) (not a solution set)
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\(-3x(5x + 9) = 0\)
- Roots are \( -3x = 0 \Rightarrow x = 0 \) and \( 5x + 9 = 0 \Rightarrow x = -\frac{9}{5} \) (not the solution set)
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\((x + 3)(9x - 5) = 0\)
- Roots are \( x + 3 = 0 \Rightarrow x = -3 \) and \( 9x - 5 = 0 \Rightarrow x = \frac{5}{9} \) (not a solution set)
-
\((x - 3)(5x + 9) = 0\)
- Roots are \( x - 3 = 0 \Rightarrow x = 3 \) and \( 5x + 9 = 0 \Rightarrow x = -\frac{9}{5} \) (this matches the given solution set)
The equation that has the solution set \( x = {-\frac{9}{5}, 3} \) is \((x - 3)(5x + 9) = 0\).
Summary
- Question 1: \(x^2 - 10 = 15\)
- Question 2: 7
- Question 3: \((x - 3)(5x + 9) = 0\)
2 answers