Question

Solve for
\[x\].
Enter the solutions from least to greatest.
\[(x -4)(-5x +1)=0\]
\[\text{lesser }x = \]
\[\text{greater } x = \]

Answer 1

To solve the equation \((x - 4)(-5x + 1) = 0\), we can apply the zero product property. This property states that if the product of two factors equals zero, then at least one of the factors must be zero.

Setting each factor equal to zero gives:

1. \(x - 4 = 0\)
2. \(-5x + 1 = 0\)

Now, we solve each equation separately.

For the first equation:
\[
x - 4 = 0
\]
Adding 4 to both sides:
\[
x = 4
\]

For the second equation:
\[
-5x + 1 = 0
\]
Subtracting 1 from both sides:
\[
-5x = -1
\]
Dividing both sides by -5:
\[
x = \frac{-1}{-5} = \frac{1}{5}
\]

Now we have the two solutions:
\[
x = \frac{1}{5} \quad \text{and} \quad x = 4
\]

Next, we arrange these solutions from least to greatest:
\(\frac{1}{5} < 4\)

Thus, we can present the solutions as follows:
\[
\text{lesser } x = \frac{1}{5}
\]
\[
\text{greater } x = 4
\]

Final answers:
\(\text{lesser } x = \frac{1}{5}\)
\(\text{greater } x = 4\)