Determine which of the values could be used to clear decimals in the given equation. \( 0.001-0.005 x=0.4 x \) 100,000 1000 100 10,000

To clear decimals in the given equation \(0.001 - 0.005x = 0.4x\), we need to multiply the entire equation by a power of 10 that will make the decimal coefficients whole numbers. This will allow us to simplify the equation and solve for \(x\). The given equation is: \(0.001 - 0.005x = 0.4x\) To clear the decimals, we need to multiply the entire equation by 1000 (since 1000 is the smallest power of 10 that will make the decimal coefficients whole numbers). Multiplying the equation by 1000 gives: \(1000 \times 0.001 - 1000 \times 0.005x = 1000 \times 0.4x\) Simplifying this gives: \(1 - 5x = 400x\) Now, we can solve this equation to find the value of \(x\). Let's solve it. Solve the equation by following steps: - step0: Solve for \(x\): \(1-5x=400x\) - step1: Move the variable to the left side: \(1-5x-400x=0\) - step2: Subtract the terms: \(1-405x=0\) - step3: Move the constant to the right side: \(-405x=0-1\) - step4: Remove 0: \(-405x=-1\) - step5: Change the signs: \(405x=1\) - step6: Divide both sides: \(\frac{405x}{405}=\frac{1}{405}\) - step7: Divide the numbers: \(x=\frac{1}{405}\) The solution to the equation \(1 - 5x = 400x\) is \(x = \frac{1}{405}\) or approximately \(x \approx 0.002469\). To clear decimals in the given equation, we need to multiply the entire equation by 1000. Therefore, the value that could be used to clear decimals in the given equation is 1000.