Certainly! Let's solve the equation step-by-step.
Given the equation:
[tex]\[ 0.25(4F - 3) = 0.05(10F - 9) \][/tex]
### Step 1: Simplify both sides of the equation
First, distribute the constants on both sides.
For the left side:
[tex]\[ 0.25(4F - 3) = 0.25 \cdot 4F - 0.25 \cdot 3 \][/tex]
[tex]\[ = 1F - 0.75 \][/tex]
[tex]\[ = F - 0.75 \][/tex]
For the right side:
[tex]\[ 0.05(10F - 9) = 0.05 \cdot 10F - 0.05 \cdot 9 \][/tex]
[tex]\[ = 0.5F - 0.45 \][/tex]
### Step 2: Set the simplified equations equal to each other
Now, equate the simplified expressions:
[tex]\[ F - 0.75 = 0.5F - 0.45 \][/tex]
### Step 3: Combine like terms to solve for [tex]\( F \)[/tex]
To isolate [tex]\( F \)[/tex], we first eliminate the terms involving [tex]\( F \)[/tex] from one side:
[tex]\[ F - 0.5F = 0.75 - 0.45 \][/tex]
[tex]\[ 0.5F = 0.3 \][/tex]
### Step 4: Solve for [tex]\( F \)[/tex]
Finally, divide both sides of the equation by 0.5 to solve for [tex]\( F \)[/tex]:
[tex]\[ F = \frac{0.3}{0.5} \][/tex]
[tex]\[ F = 0.6 \][/tex]
### Conclusion
The solution to the equation [tex]\( 0.25(4F - 3) = 0.05(10F - 9) \)[/tex] is:
[tex]\[ F = 0.6 \][/tex]
