\( \frac { 3 } { 4 } x + \frac { 1 } { 3 } ; \frac { 5 } { 6 } x - \frac { 7 } { 6 } \)

To solve for \( x \) in the equation \( \frac { 3 } { 4 } x + \frac { 1 } { 3 } = \frac { 5 } { 6 } x - \frac { 7 } { 6 } \), start by bringing all terms involving \( x \) to one side and constant terms to the other. First, we're going to get all the \( x \) terms on one side and constants on the other side. This can involve finding a common denominator to simplify the fractions. Next, after rearranging, you can isolate \( x \) by combining like terms and solving the resulting equation. Typically, this involves multiplying through by a common denominator to eliminate the fractions, making calculations simpler. Once you find \( x \), don't forget to double-check your work by plugging it back into the original equation! When rational expressions are involved like in this equation, it’s crucial to keep an eye on your fractions! One common mistake can be forgetting to multiply each term by the common denominator, which can lead to incorrect simplifications or missed solutions. Always double-check your calculations!