Solving Inequalities Review

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation [-5, ∞) represent?

Back

It represents all real numbers greater than or equal to -5.

Front

How do you solve the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3.

Front

What is the solution to the absolute-value inequality |2x - 11| < 21?

Back

The solution is 5 < x < 16.

Front

How do you solve the inequality 6 - 2|m - 3| > -4?

Back

First, isolate the absolute value: 6 + 4 > 2|m - 3|. Then, 10 > 2|m - 3|, which simplifies to 5 > |m - 3|. This leads to -2 < m < 8.

Front

What does the inequality 4x < 4(x - 1) simplify to?

Back

It simplifies to 4x < 4x - 4, which leads to no solutions.

Front

What is the difference between a closed interval and an open interval?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not (e.g., (a, b)).

Front

What does the symbol '≤' mean in inequalities?

Back

It means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

What is the graphical representation of the inequality x > 3?

Back

It is represented by an open circle at 3 and a line extending to the right.

Front

How do you express the solution set of x < -2 in interval notation?

Back

The solution set is expressed as (-∞, -2).