Algebra: Review of Inequalities and Absolute Value

Front

What is an inequality?

Back

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

Front

What does |x| represent?

Back

|x| represents the absolute value of x, which is the distance of x from 0 on the number line, regardless of direction.

Front

How do you solve the inequality |x - 3| < 5?

Back

To solve |x - 3| < 5, split it into two inequalities: -5 < x - 3 < 5, which simplifies to -2 < x < 8.

Front

What is the solution to the equation |x + 2| = 4?

Back

The solutions are x + 2 = 4 or x + 2 = -4, which gives x = 2 or x = -6.

Front

What does the symbol ≤ mean?

Back

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

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.

Front

How do you graph the inequality x > 3?

Back

Graph a number line, place an open circle at 3, and shade to the right to indicate all numbers greater than 3.

Front

What is the solution set for the inequality |x - 1| ≥ 2?

Back

The solution set is x ≤ -1 or x ≥ 3.

Front

How do you interpret the inequality 2x + 10 ≤ 25?

Back

This means that the total cost of games (2x) plus $10 for food must be less than or equal to $25.

Front

What is the solution to the equation |b + 4| - 4 = 0?

Back

The solutions are b + 4 = 4 or b + 4 = -4, which gives b = 0 or b = -8.