Intermediate Algebra (6th Edition)

$(-25,∞)$
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.