Which value of x satisfies the equation (5)/(2)(x+(5)/(6))=-(65)/(12) ? 2 3 -3 -2

Simplify Equation: First, we need to simplify the equation and isolate x. Let's start by simplifying the left side of the equation. (5)/(2)(x+(5)/(6)) = (5/2) * (x + 5/6) To simplify further, we can find a common denominator for the terms inside the parentheses.Find Common Denominator: The common denominator for x and 5/6 is 6. So we rewrite x as (6x/6). (5/2) * ((6x/6) + (5/6)) = (5/2) * ((6x + 5)/6) Now we can combine the terms inside the parentheses.Combine Terms: Multiplying the numerator of the first fraction by the numerator of the second fraction, we get: (5 * (6x + 5))/(2 * 6) = (30x + 25)/12 Now we have the left side of the equation simplified.Equate Left and Right Side: Next, we equate the simplified left side to the right side of the equation: (30x + 25)/12 = -(65)/12 Since the denominators are the same, we can equate the numerators. 30x + 25 = -65Subtract 25: Now, we solve for x by subtracting 25 from both sides of the equation. 30x + 25 - 25 = -65 - 25 30x = -90Divide by 30: Finally, we divide both sides by 30 to isolate x. 30x/30 = -90/30 x = -3

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Q. Which value of

x

satisfies the equation

\frac{5}{2}\left(x+\frac{5}{6}\right)=-\frac{65}{12}

\newline

2

\newline

3

\newline

-3

\newline

-2

Simplify Equation: First, we need to simplify the equation and isolate $x$ . Let's start by simplifying the left side of the equation. $\frac{5}{2}(x+\frac{5}{6}) = \frac{5}{2} \times (x + \frac{5}{6})$ To simplify further, we can find a common denominator for the terms inside the parentheses.
Find Common Denominator: The common denominator for $x$ and $\frac{5}{6}$ is $6$ . So we rewrite $x$ as $(\frac{6x}{6})$ .
$(\frac{5}{2}) \cdot ((\frac{6x}{6}) + (\frac{5}{6})) = (\frac{5}{2}) \cdot (\frac{6x + 5}{6})$
Now we can combine the terms inside the parentheses.
Combine Terms: Multiplying the numerator of the first fraction by the numerator of the second fraction, we get: $\newline$ $(5 \times (6x + 5))/(2 \times 6) = (30x + 25)/12$ $\newline$ Now we have the left side of the equation simplified.
Equate Left and Right Side: Next, we equate the simplified left side to the right side of the equation: $\newline$ $(30x + 25)/12 = -(65)/12$ $\newline$ Since the denominators are the same, we can equate the numerators. $\newline$ $30x + 25 = -65$
Subtract $25$ : Now, we solve for $x$ by subtracting $25$ from both sides of the equation. $30x + 25 - 25 = -65 - 25$ $30x = -90$
Divide by $30$ : Finally, we divide both sides by $30$ to isolate $x$ . $\frac{30x}{30} = \frac{-90}{30}$ $x = -3$