Answer
$(-25,∞)$
Work Step by Step
We are given that $3x+10\gt\frac{5}{2}(x-1)$.
We can solve for x by first using the distributive property to simplify the right side.
$3x+10\gt\frac{5}{2}x-\frac{5}{2}$
Add $\frac{5}{2}$ to both sides.
$3x+\frac{25}{2}\gt\frac{5}{2}x$
Subtract 3x from both sides.
$\frac{25}{2}\gt-\frac{1}{2}x$
Multiply both sides by 2.
$25\gt-x$
Divide both sides by -1 (which will reverse the inequality sign).
$x\gt-25$
Therefore, the inequality will be satisfied for all values of x greater than -25.
