Question

Evaluate: Step 1 Step 2: True or False Statement?
(2x−7)(x+9)=0
original question
0 (2(0)−7)((0+9)=0
(−7)(9)=0

Answer 1

To evaluate the equation \((2x - 7)(x + 9) = 0\) and confirm the steps you provided, let's first solve the equation step-by-step.

1. **Set Each Factor to Zero:**
The equation \((2x - 7)(x + 9) = 0\) implies that at least one of the factors must be zero. Therefore, we can set each factor to zero:
- \(2x - 7 = 0\)
- \(x + 9 = 0\)

2. **Solve Each Equation:**
From \(2x - 7 = 0\):
\[
2x = 7 \quad \Rightarrow \quad x = \frac{7}{2}
\]

From \(x + 9 = 0\):
\[
x = -9
\]

So the solutions to the equation \((2x - 7)(x + 9) = 0\) are \(x = \frac{7}{2}\) or \(x = -9\).

Now, let’s evaluate the statement you provided in Step 2:

You substituted \(x = 0\) into the factors:
\[
(2(0) - 7)(0 + 9) = (-7)(9) = -63
\]
This shows that the left side does not equal \(0\) (since \(-63 \neq 0\)).

So, the statement that \((2(0) - 7)(0 + 9) = 0\) is **False**.

Final answer: **False**.