Question

Solve -3(x – 10) > -x + 5. Write your solution using set builder notation. Please show all of your work.

Answer 1

You are given the inequality (I simplified it a bit)\[3(10-x)>5-x.\]Solve it just like you would any other equation:\[30-3x>5-x,\]\[25>2x,\]\[\frac{25}{2}>x.\]Simply enough, the solution set can be expressed using set-builder notation as follows: \(\{x\in\mathbb{R}:x<25/2\}\).