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a)
(2x-5)/(4)-(x-4)/(3)=(x)/(4)

a) $\frac{2 x-5}{4}-\frac{x-4}{3}=\frac{x}{4}$

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Multiplication with rational exponents

Full solution

Q. a)

\frac{2 x-5}{4}-\frac{x-4}{3}=\frac{x}{4}

Find Common Denominator: Step $1$ : Find a common denominator for the fractions to combine them. $\newline$ Common denominator of $4$ and $3$ is $12$ . $\newline$ $\frac{2x-5}{4} \times \frac{3}{3} - \frac{x-4}{3} \times \frac{4}{4} = \frac{x}{4} \times \frac{12}{12}$ $\newline$ = $\frac{6x-15}{12} - \frac{4x-16}{12} = \frac{3x}{12}$
Combine Fractions: Step $2$ : Combine the fractions on the left side. $\newline$ $(6x - 15 - 4x + 16) / 12 = 3x / 12$ $\newline$ $= (2x + 1) / 12 = 3x / 12$
Clear Denominators: Step $3$ : Simplify the equation by multiplying all terms by $12$ to clear the denominators. $12 \times \left(\frac{2x + 1}{12}\right) = 12 \times \left(\frac{3x}{12}\right)$ $2x + 1 = 3x$
Solve for x: Step $4$ : Solve for x. $\newline$ $2x + 1 = 3x$ $\newline$ $1 = 3x - 2x$ $\newline$ $1 = x$

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