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 3x−142=−4\frac{3x - 14}{2} = -4, first eliminate the denominator by multiplying both sides of the equation by 2:

3x−142⋅2=−4⋅2 \frac{3x - 14}{2} \cdot 2 = -4 \cdot 2

This simplifies to:

3x−14=−8 3x - 14 = -8

Step 2: Isolate the variable term

Next, isolate the term containing xx by adding 14 to both sides of the equation:

3x−14+14=−8+14 3x - 14 + 14 = -8 + 14

This simplifies to:

3x=6 3x = 6

Step 3: Solve for xx

Finally, solve for xx by dividing both sides of the equation by 3:

3x3=63 \frac{3x}{3} = \frac{6}{3}

This simplifies to:

x=2 x = 2

Final Answer

x=2 \boxed{x = 2}

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