Solve for x. 40= x/(-4/7)

Solve for x. 40= x/(-4/7)

The Correct Answer and Explanation is:

To solve for (x) in the equation:

[
40 = \frac{x}{-\frac{4}{7}}
]

Follow these steps:

Step 1: Understand the equation

The equation is:

[
40 = \frac{x}{-\frac{4}{7}}
]

This means that 40 is equal to (x) divided by (-\frac{4}{7}). To solve for (x), we need to isolate (x) on one side of the equation.

Step 2: Eliminate the denominator

To eliminate the fraction in the denominator, we multiply both sides of the equation by (-\frac{4}{7}). This will cancel out the denominator on the right-hand side. Here’s how:

[
40 \times \left(-\frac{4}{7}\right) = \frac{x}{-\frac{4}{7}} \times \left(-\frac{4}{7}\right)
]

The (-\frac{4}{7}) on the right side cancels out, leaving just (x), and on the left side, we have:

[
x = 40 \times \left(-\frac{4}{7}\right)
]

Step 3: Multiply the terms

Now, perform the multiplication:

[
40 \times \left(-\frac{4}{7}\right) = \frac{40 \times -4}{7} = \frac{-160}{7}
]

Step 4: Simplify the result

The result is:

[
x = \frac{-160}{7}
]

This is the exact value of (x), and it can be left as a fraction. However, if we want a decimal approximation, we divide (-160) by 7:

[
x \approx -22.86
]

Final Answer:

The solution to the equation is:

[
x = \frac{-160}{7} \quad \text{or approximately} \quad x \approx -22.86
]

Explanation:

This is a straightforward algebraic equation that involves a fraction. To solve it, we utilized the property that dividing by a fraction is equivalent to multiplying by its reciprocal. This method of multiplying both sides of the equation by the reciprocal of (-\frac{4}{7}) isolates (x), leading to the solution.