Q. Solve the Equation \( 1.25x – 0.35x = 585 \) for \( x \)

Write the original equation.

\(1.25x – 0.35x = 585\)

Factor out the common factor \(x\) from the left-hand side. When two terms share the same variable factor, you can factor it: \(ax – bx = (a – b)x\).

\((1.25 – 0.35)x = 585\)

Compute the difference of the coefficients on the left-hand side. Subtract \(0.35\) from \(1.25\).

\(1.25 – 0.35 = 0.90\)

So the equation becomes

\(0.90x = 585\)

Isolate \(x\) by dividing both sides of the equation by the coefficient \(0.90\). Division by a nonzero number is the inverse operation of multiplication and yields the value of \(x\).

\(x = \dfrac{585}{0.90}\)

Simplify the fraction. To avoid decimals, multiply numerator and denominator by 100 (or recognize that dividing by 0.90 is the same as dividing by 9/10, i.e., multiplying by 10/9).

\(x = \dfrac{585}{0.90} = \dfrac{585}{9/10} = 585 \times \dfrac{10}{9}\)

Compute \(585 \times \dfrac{10}{9}\). First divide \(585\) by \(9\): \(585 \div 9 = 65\). Then multiply by \(10\): \(65 \times 10 = 650\).

State the final answer.

\(x = 650\)