To solve the equation [tex]\((3x + 2)(x - 5) = 0\)[/tex], we can use the property of zero products. This property states that if the product of two factors is zero, then at least one of the factors must be zero.
So, we need to solve each factor for [tex]\( x \)[/tex]:
1. [tex]\(3x + 2 = 0\)[/tex]
2. [tex]\(x - 5 = 0\)[/tex]
### Solving the first factor:
1. [tex]\(3x + 2 = 0\)[/tex]
2. Subtract 2 from both sides: [tex]\(3x = -2\)[/tex]
3. Divide both sides by 3: [tex]\(x = -\frac{2}{3}\)[/tex]
So, the first root is [tex]\(x = -\frac{2}{3}\)[/tex].
### Solving the second factor:
1. [tex]\(x - 5 = 0\)[/tex]
2. Add 5 to both sides: [tex]\(x = 5\)[/tex]
So, the second root is [tex]\(x = 5\)[/tex].
The solutions to the equation [tex]\((3x + 2)(x - 5) = 0\)[/tex] are [tex]\(x = -\frac{2}{3}\)[/tex] and [tex]\(x = 5\)[/tex].
### Identify the solution with the highest value:
The solutions we found are:
1. [tex]\(x = -\frac{2}{3}\)[/tex] (approximately -0.6667)
2. [tex]\(x = 5\)[/tex]
Clearly, [tex]\(x = 5\)[/tex] is the highest value.
Answer: The solution with the highest value is [tex]\(x = 5\)[/tex].
