Chapter 3 Test _ Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' represent?

Back

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

Front

How do you solve the inequality 4x ≤ x?

Back

To solve 4x ≤ x, subtract x from both sides to get 3x ≤ 0, then divide by 3 to find x ≤ 0.

Front

What is the first step in solving the inequality |x + 4| - 8 > 2?

Back

The first step is to add 8 to both sides, resulting in |x + 4| > 10.

Front

What does the absolute value of a number represent?

Back

The absolute value of a number represents its distance from zero on the number line, regardless of direction.

Front

How do you interpret the inequality 10 ≥ x - 3?

Back

To interpret 10 ≥ x - 3, you can add 3 to both sides to find x ≤ 13.

Front

What is the solution to the inequality 3x < 6?

Back

To solve 3x < 6, divide both sides by 3 to find x < 2.

Front

What is the significance of the solution x < 2 in an inequality?

Back

The solution x < 2 indicates that any value less than 2 satisfies the inequality.

Front

What is the process for solving compound inequalities?

Back

To solve compound inequalities, solve each part separately and then combine the solutions, ensuring to consider the logical connections (AND/OR) between them.

Front

What does it mean to graph an inequality on a number line?

Back

Graphing an inequality on a number line involves shading the region that represents all possible solutions and using open or closed circles to indicate whether endpoints are included.