Questions: Solving a multi-step equation given in fractional form Solve for x. (3x-14)/2 = -4 Simplify your answer as much as possible. x=

Solving a multi-step equation given in fractional form Solve for x. (3x-14)/2 = -4 Simplify your answer as much as possible. x=
Transcript text: Solving a multi-step equation given in fractional form Solve for $x$. \[ \frac{3 x-14}{2}=-4 \] Simplify your answer as much as possible. \[ x= \]
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Solution

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Solution Steps

Step 1: Eliminate the denominator

To solve the equation \(\frac{3x - 14}{2} = -4\), first eliminate the denominator by multiplying both sides of the equation by 2:

\[ \frac{3x - 14}{2} \cdot 2 = -4 \cdot 2 \]

This simplifies to:

\[ 3x - 14 = -8 \]

Step 2: Isolate the variable term

Next, isolate the term containing \(x\) by adding 14 to both sides of the equation:

\[ 3x - 14 + 14 = -8 + 14 \]

This simplifies to:

\[ 3x = 6 \]

Step 3: Solve for \(x\)

Finally, solve for \(x\) by dividing both sides of the equation by 3:

\[ \frac{3x}{3} = \frac{6}{3} \]

This simplifies to:

\[ x = 2 \]

Final Answer

\[ \boxed{x = 2} \]

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