Simplify and solve the following linear equation: $0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$
Answer
Verified
Hint: Remove the brackets and solve for the unknown.
The given equation is $0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$ First let us expand the brackets. Expanding the brackets, we get $\begin{gathered} 0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right) \\ 0.25\left( {4f} \right) - 3\left( {0.25} \right) = 0.05\left( {10f} \right) - 9\left( {0.05} \right) \\ f - 0.75 = 0.5f - 0.45 \\ \end{gathered} $ Rearranging the equation by combining the like terms and the constants, we get $\begin{gathered} f - 0.5f = 0.75 - 0.45 \\ 0.5f = 0.30 \\ \end{gathered} $ Multiplying both sides by 10 to remove the decimals for easier calculation, $\begin{gathered} 5f = 3 \\ f = \dfrac{3}{5} \\ \end{gathered} $ Since the equation is given in decimal, we will find the decimal value too for$f$. Hence,$f = \dfrac{3}{5} = 0.6$ Note: To check if the answer is correct, substitute the value of back into the given equation and check if you get LHS=RHS. The process of simplifying a linear is just arranging all the like terms to one side and the constants to the other side and solving for the unknown value.
×
Sorry!, This page is not available for now to bookmark.