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

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

Transcript text: Solve for $m$. \[ \begin{array}{l} \frac{5}{4} m-2=-m+\frac{1}{2}-\frac{7}{4}+\frac{1}{2} m \\ m=\square \end{array} \] Submit

Solution

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.

Step 1: Set Up the Equation

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

Step 2: Simplify Both Sides

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: \[ \frac{5}{4} m - 2 = -\frac{1}{2} m - \frac{5}{4} \]

Step 3: Combine Like Terms

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: \[ \frac{7}{4} m = \frac{3}{4} \]

Step 4: Solve for $ m $

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