# Simplify and solve the following linear equation:

$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$

Answer

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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.

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.

Last updated date: 25th Sep 2023

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