Question
1) \( \begin{aligned}(2 x+3)(5 x+1) & =0 \\ \text { 1) }(x-3)(x+9) & =0\end{aligned} \)
Ask by Simpson Beck. in South Africa
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are:
- For (2x + 3)(5x + 1) = 0: x = -3/2 or x = -1/5
- For (x - 3)(x + 9) = 0: x = 3 or x = -9
Solution
Let's solve each equation step by step:
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Equation 1: (2x + 3)(5x + 1) = 0
Using the zero product property, set each factor equal to zero:
1. 2x + 3 = 0
Subtract 3: 2x = -3
Divide by 2: x = -3/2
2. 5x + 1 = 0
Subtract 1: 5x = -1
Divide by 5: x = -1/5
So, the solutions for the first equation are x = -3/2 and x = -1/5.
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Equation 2: (x - 3)(x + 9) = 0
Again, apply the zero product property:
1. x - 3 = 0
Add 3: x = 3
2. x + 9 = 0
Subtract 9: x = -9
Thus, the solutions for the second equation are x = 3 and x = -9.
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Summary of Solutions:
• For (2x + 3)(5x + 1) = 0:
x = -3/2 or x = -1/5
• For (x - 3)(x + 9) = 0:
x = 3 or x = -9
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Simplify this solution Mind Expander
To solve the first equation \( (2x + 3)(5x + 1) = 0 \), we set each factor to zero. This gives us \( 2x + 3 = 0 \) leading to \( x = -\frac{3}{2} \), and \( 5x + 1 = 0 \) giving \( x = -\frac{1}{5} \). For the second equation \( (x - 3)(x + 9) = 0 \), we set each factor equal to zero as well. This results in \( x - 3 = 0 \) which gives \( x = 3 \), and \( x + 9 = 0 \) leading to \( x = -9 \). Now you have four distinct solutions: \( x = -\frac{3}{2}, -\frac{1}{5}, 3, \) and \( -9 \)!
