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c.

(5(x+3))/(2)=(x)/(3)

c. $\newline$ $\frac{5(x+3)}{2}=\frac{x}{3}$

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Add and subtract polynomials

Full solution

Q. c.

\newline

\frac{5(x+3)}{2}=\frac{x}{3}

Eliminate Fractions: First, we need to eliminate the fractions by finding a common denominator and multiplying both sides of the equation by that common denominator. The common denominator for $2$ and $3$ is $6$ . We will multiply both sides of the equation by $6$ to clear the fractions. $\newline$ $(6) \times \frac{5(x+3)}{2} = (6) \times \frac{x}{3}$
Simplify Equation: Now, we simplify both sides of the equation. On the left side, the $6$ and $2$ will cancel out, leaving us with $3 \times (5(x+3))$ . On the right side, the $6$ and $3$ will cancel out, leaving us with $2x$ . $\newline$ $3 \times (5(x+3)) = 2x$
Distribute and Combine: Next, we distribute the $3$ into the parentheses on the left side of the equation. $3 \times 5x + 3 \times 3 = 2x$ $15x + 9 = 2x$
Rearrange Terms: Now, we want to get all the $x$ terms on one side and the constants on the other side. We can do this by subtracting $2x$ from both sides of the equation. $15x + 9 - 2x = 2x - 2x$ $13x + 9 = 0$
Correct Mistake: We made a mistake in the previous step. We should have subtracted $2x$ from both sides to get the $x$ terms on one side, but we incorrectly set the right side to $0$ . Let's correct this. $\newline$ $15x + 9 - 2x = 2x - 2x$ $\newline$ $13x + 9 = 0x$ $\newline$ $13x + 9 = 0$

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