)) Solve for (5)/(4)m-2=-m+(1)/(2)-(7)/(4)+(1)/(2)m m square

To solve the equation \(\frac{5}{4}m - 2 = -m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2}m\), we first need to simplify and combine like terms on both sides of the equation.<br /><br />Starting with the right side of the equation:<br />\[<br />-m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2}m<br />\]<br /><br />Combine the \(m\) terms:<br />\[<br />-m + \frac{1}{2}m = -\frac{1}{2}m<br />\]<br /><br />Combine the constant terms:<br />\[<br />\frac{1}{2} - \frac{7}{4} = \frac{2}{4} - \frac{7}{4} = -\frac{5}{4}<br />\]<br /><br />So the right side simplifies to:<br />\[<br />-\frac{1}{2}m - \frac{5}{4}<br />\]<br /><br />Now, rewrite the equation with the simplified right side:<br />\[<br />\frac{5}{4}m - 2 = -\frac{1}{2}m - \frac{5}{4}<br />\]<br /><br />Next, we'll move all the \(m\) terms to one side and the constant terms to the other side. Add \(\frac{1}{2}m\) to both sides:<br />\[<br />\frac{5}{4}m + \frac{1}{2}m - 2 = -\frac{5}{4}<br />\]<br /><br />Combine the \(m\) terms on the left side:<br />\[<br />\frac{5}{4}m + \frac{2}{4}m = \frac{7}{4}m<br />\]<br /><br />So the equation now is:<br />\[<br />\frac{7}{4}m - 2 = -\frac{5}{4}<br />\]<br /><br />Next, add 2 to both sides to isolate the \(m\) term:<br />\[<br />\frac{7}{4}m = -\frac{5}{4} + 2<br />\]<br /><br />Convert 2 to a fraction with a common denominator:<br />\[<br />2 = \frac{8}{4}<br />\]<br /><br />So:<br />\[<br />-\frac{5}{4} + \frac{8}{4} = \frac{3}{4}<br />\]<br /><br />Now the equation is:<br />\[<br />\frac{7}{4}m = \frac{3}{4}<br />\]<br /><br />To solve for \(m\), multiply both sides by the reciprocal of \(\frac{7}{4}\):<br />\[<br />m = \frac{3}{4} \times \frac{4}{7} = \frac{3}{7}<br />\]<br /><br />Thus, the solution is:<br />\[<br />m = \frac{3}{7}<br />\]