inequality mixed review

Front

What is an inequality?

Back

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

Front

How do you solve the inequality 5x + 10 ≥ 100?

Back

Subtract 10 from both sides to get 5x ≥ 90, then divide by 5 to find x ≥ 18.

Front

What does the absolute value notation |x| represent?

Back

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

Front

How do you solve the equation |4x - 3| = 17?

Back

Set up two equations: 4x - 3 = 17 and 4x - 3 = -17. Solve both to find x = 5 and x = -3.5.

Front

What is the solution set for the inequality |x - 2| > 3?

Back

The solution set is x < -1 or x > 5.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Front

What is the graphical representation of the inequality x < 2?

Back

The graph shows a number line with an open circle at 2 and shading to the left.

Front

How do you represent the solution to the inequality -8x < 48?

Back

Divide by -8 and flip the sign to get x > -6.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include it.

Front

What does the inequality 5x + 10 > 100 represent in a real-world context?

Back

It represents a situation where a person needs to earn more than $90 to afford an item costing $100 after receiving $10.