Solve the linear equation: 0.25(4f - 3) = 0.05(10f - 9).

• A) f = 2/15
• B) f = 9/4
• C) f = 2/7
• D) f = 3/5

To solve the equation \(0.25(4f - 3) = 0.05(10f - 9)\), we will first simplify both sides.

Step 1: Distribute the Constants

Start by distributing the constants on both sides:

• Left side: \(0.25 \times 4f - 0.25 \times 3 = f - 0.75\)
• Right side: \(0.05 \times 10f - 0.05 \times 9 = 0.5f - 0.45\)

Step 2: Set the Equation

Now, we rewrite the equation:

f - 0.75 = 0.5f - 0.45

Step 3: Rearranging the Equation

Next, we will move all terms involving \(f\) to one side and constant terms to the other side:

• Subtract \(0.5f\) from both sides: \(f - 0.5f = 0.75 - 0.45\)
• This simplifies to: \(0.5f = 0.3\)

Step 4: Solve for \(f\)

Now, divide both sides by \(0.5\):

f = \frac{0.3}{0.5} = 0.6

Step 5: Convert to Fraction

To express \(0.6\) as a fraction, we have:

f = \frac{6}{10} = \frac{3}{5}

Final Answer

The solution to the equation is:

f = 3/5