Questions: Solve the equation for x : (x+2) / 4-(x-1) / 3=2 Write your answer as a simplified fraction, if applicable. For example, 5/9.

Solve the equation for x : (x+2) / 4-(x-1) / 3=2 Write your answer as a simplified fraction, if applicable. For example, 5/9.
Transcript text: Solve the equation for $x$ : \[ (x+2) / 4-(x-1) / 3=2 \] Write your answer as a simplified fraction, if applicable. For example, 5/9.
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Solution

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Solution Steps

To solve the equation \(\frac{x+2}{4} - \frac{x-1}{3} = 2\), we need to find a common denominator for the fractions, combine them, and then solve for \(x\). Finally, simplify the result to get the answer in the form of a fraction.

Step 1: Combine the Fractions

To solve the equation \(\frac{x+2}{4} - \frac{x-1}{3} = 2\), we first find a common denominator for the fractions. The common denominator of 4 and 3 is 12.

\[ \frac{x+2}{4} = \frac{3(x+2)}{12} = \frac{3x + 6}{12} \]

\[ \frac{x-1}{3} = \frac{4(x-1)}{12} = \frac{4x - 4}{12} \]

Step 2: Combine the Fractions

Now, we combine the fractions:

\[ \frac{3x + 6}{12} - \frac{4x - 4}{12} = \frac{(3x + 6) - (4x - 4)}{12} = \frac{3x + 6 - 4x + 4}{12} = \frac{-x + 10}{12} \]

Step 3: Set the Equation Equal to 2

We set the combined fraction equal to 2:

\[ \frac{-x + 10}{12} = 2 \]

Step 4: Solve for \(x\)

To solve for \(x\), we multiply both sides by 12:

\[ -x + 10 = 24 \]

Subtract 10 from both sides:

\[ -x = 14 \]

Multiply both sides by -1:

\[ x = -14 \]

Final Answer

\(\boxed{x = -14}\)

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