Solving Multistep Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

Front

What does the notation [-2, 5] represent?

Back

The notation [-2, 5] represents the set of all real numbers x such that -2 ≤ x ≤ 5.

Front

How do you graph the inequality x > 3?

Back

To graph x > 3, draw a number line, place an open circle at 3, and shade to the right.

Front

What is the solution to the inequality |x + 4| - 8 > 2?

Back

The solution is x > 6 or x < -14.

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 does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include endpoints (e.g., (a, b)), while closed intervals do include endpoints (e.g., [a, b]).

Front

How do you express the solution -8 ≤ x < 8 in interval notation?

Back

The solution in interval notation is [-8, 8).