Questions: Solve for (m). [ frac54 m-2=-m+frac12-frac74+frac12 m m=square ]

Solution Steps

To solve for $m$, we need to simplify both sides of the equation and then isolate $m$. Start by combining like terms on both sides of the equation. Once simplified, move all terms involving $m$ to one side and constant terms to the other side. Finally, solve for $m$ by dividing or multiplying as necessary.

We start with the equation: $$\frac{5}{4} m - 2 = -m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2} m$$

First, we simplify the right side: $$-m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2} m = -m + \frac{2}{4} - \frac{7}{4} + \frac{2}{4} m = (-1 + \frac{1}{2}) m - \frac{5}{4} = -\frac{1}{2} m - \frac{5}{4}$$ Thus, the equation becomes: $$\frac{5}{4} m - 2 = -\frac{1}{2} m - \frac{5}{4}$$

Next, we move all terms involving $m$ to one side and constant terms to the other side: $$\frac{5}{4} m + \frac{1}{2} m = -\frac{5}{4} + 2$$ Converting $2$ to a fraction gives us: $$2 = \frac{8}{4}$$ So, we have: $$\frac{5}{4} m + \frac{2}{4} m = \frac{3}{4}$$ This simplifies to: $$\frac{7}{4} m = \frac{3}{4}$$

To isolate $m$, we multiply both sides by $\frac{4}{7}$: $$m = \frac{3}{4} \cdot \frac{4}{7} = \frac{3}{7}$$

Final Answer