Question

How do you solve (x-3)/(2x+5) >= 1?

Answer 1

Subtract 1 from both sides to get (x-3)/(2x+5)-1>=0. Get a common denominator of (2x+5) so that your equation reads (-x-8)/(2x+5)>=0. This gives you two points of interest: x=-8 and x=-2.5. Investigating the sign (+ or -) around those points yields the result that only [-8,-2.5) produces values where (x-3)/(2x+5)>=1.

Answer 2

You're welcome.

Answer 3

*Thank you!

Answer 4

Why is there a bracket on the -8 and parentheses on -2.5?

Answer 5

Good question: it is because -8 actually solves the inequality (giving 1 >= 1), whereas -2.5 makes the denominator zero, meaning it is not a solution. Visually, -8 would be a closed dot, whereas -2.5 would be an open dot.