Linear Inequalities - Chap. 5 Review

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a range of possible solutions rather than a single solution.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side of the inequality can be either greater than or equal to the value on the right side.

Front

How do you graph the inequality x ≥ -4?

Back

To graph x ≥ -4, draw a number line, place a closed circle on -4 (indicating -4 is included), and shade the line to the right to show all values greater than -4.

Front

What is the solution to the inequality -3x > 9?

Back

To solve -3x > 9, divide both sides by -3 (remember to flip the inequality sign): x < -3.

Front

How do you write a linear inequality from a word problem?

Back

Identify the variable, determine the relationship described in the problem, and express it using an inequality symbol based on the context (e.g., 'at least', 'at most').

Front

Write the linear inequality for: 'A baker needs at least 25 pounds of flour and has 7 pounds.'

Back

The inequality is x + 7 ≥ 25, where x is the amount of flour needed.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents a line with a slope of 2 and a y-intercept of 3, with the area below the line shaded, indicating all points (x, y) that satisfy the inequality.

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line (since it's <), and shade below the line to represent all solutions.

Front

What does the symbol '<' mean in a linear inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is strictly less than the value on the right side.

Front

Write the linear inequality for: 'A school club can spend at most $200 and has spent $85.'

Back

The inequality is x + 85 ≤ 200, where x is the amount they can still spend.