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(2x+7)/(3)-(x-3)/(2)=4x

$\frac{2 x+7}{3}-\frac{x-3}{2}=4 x$

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Add and subtract polynomials

Full solution

Q.

\frac{2 x+7}{3}-\frac{x-3}{2}=4 x

Find Common Denominator: Find a common denominator for the fractions to combine them. $\newline$ The common denominator for $3$ and $2$ is $6$ . We will multiply each term by $6$ to eliminate the denominators. $\newline$ $\frac{2x+7}{3} \times 6 - \frac{x-3}{2} \times 6 = 4x \times 6$
Distribute $6$ to Numerators: Distribute the $6$ to each term in the numerators. $\newline$ $(2x+7) \times 2 - (x-3) \times 3 = 24x$ $\newline$ $4x + 14 - 3x + 9 = 24x$
Combine Like Terms: Combine like terms. $\newline$ $4x + 14 - 3x + 9 = 24x$ $\newline$ $(4x - 3x) + (14 + 9) = 24x$ $\newline$ $x + 23 = 24x$
Move Terms with x: Move all terms containing x to one side of the equation. $\newline$ $x - 24x + 23 = 0$ $\newline$ $-23x + 23 = 0$
Isolate x: Isolate x by moving the constant term to the other side. $\newline$ $-23x = -23$
Divide by $-23$ : Divide both sides by $-23$ to solve for $x$ . $x = \frac{-23}{-23}$ $x = 1$

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