#### Answer

x = $\frac{5}{6}$

#### Work Step by Step

$\frac{5}{2}x - 1 = x + \frac{1}{4}$
Subtract x from both sides:
$\frac{3}{2}x - 1 = \frac{1}{4}$
Add 1 to both sides:
$\frac{3}{2}x = 1 \frac{1}{4}$
Multiply both sides by the reciprocal of the coefficient, $\frac{2}{3}$
$\frac{2}{3}(\frac{3}{2}x) = (1 \frac{1}{4})\frac{2}{3}$
Simplify:
x = $(\frac{5}{4})\frac{2}{3}$
x = $\frac{5}{6}$