
Solving Inequalities
Goals
You will learn (review) to
• understand inequalities analytically (with symbolic expressions),
graphically, and verbally.
• solve linear inequalities;
• solve absolutevalue inequalities;
• solve quadratic inequalities;
• solve combined inequalities;
• use inequalities for mathematical modeling.
Practice Problems
Problem 1 Use the graph below to answer the following. Approximate to
the nearest 0.1 unit. Write answers in both interval and inequality
notation.
(a) f(x) ≥ 0
(b) f(x) ≤g(x)
(c) f(x)g(x) > 0
Problem 2 Write as an inequality: “u is more than 5 units from −1.”
Graph the solution set, express the solution set in interval and inequality
notation (different from the original inequality).
Problem 3 Solve each inequality. Express the solution
using set notation,
interval notation, and a graph.
(a) x − 5 < −4
(b) 7 − 2x ≥ 3
(c) −5 ≤ 4 − 7x < 17
Problem 4
