Sure, let's solve the equation [tex]\((2x + 7)(x - 1) = 0\)[/tex].
We begin by using the property of the zero product rule, which states that if a product of two factors equals zero, then at least one of the factors must be zero.
So, we set each factor equal to zero and solve for [tex]\(x\)[/tex].
1. Set the first factor equal to zero:
[tex]\[
2x + 7 = 0
\][/tex]
To solve for [tex]\(x\)[/tex], we first isolate [tex]\(2x\)[/tex] by subtracting 7 from both sides:
[tex]\[
2x = -7
\][/tex]
Next, we divide both sides by 2:
[tex]\[
x = -\frac{7}{2}
\][/tex]
2. Set the second factor equal to zero:
[tex]\[
x - 1 = 0
\][/tex]
To solve for [tex]\(x\)[/tex], we add 1 to both sides:
[tex]\[
x = 1
\][/tex]
Therefore, the solutions to the equation [tex]\((2x + 7)(x - 1) = 0\)[/tex] are:
[tex]\[
x = -\frac{7}{2} \quad \text{and} \quad x = 1
\][/tex]
These are the points where the original equation holds true.
