Simplify and solve the following linear equation:
$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$

Question

Simplify and solve the following linear equation:$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$

Vedantu Content Team · Accepted Answer

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.

Simplify and solve the following linear equation:
$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$

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Simplify and solve the following linear equation:$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$

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NCERT Book Solutions

Reference Book Solutions

Question Papers

Exams

Quick Links

Simplify and solve the following linear equation:
$0.25\left( {4f - 3} \right) = 0.05\left( {10f - 9} \right)$