Ch. 2 Test: Solving Inequalities

Front

What does an open circle represent when graphing inequalities?

Back

An open circle indicates that the number is not included in the solution set (e.g., for b < 6, 6 is not included).

Front

What does a closed circle represent when graphing inequalities?

Back

A closed circle indicates that the number is included in the solution set (e.g., for x ≤ 5, 5 is included).

Front

How do you solve the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77; then divide by 7: n > 11.

Front

What is the solution to the inequality x ≤ -11?

Back

The solution set includes all numbers less than or equal to -11.

Front

How do you graph the inequality x < 4?

Back

Draw a number line, place an open circle at 4, and shade to the left.

Front

What is the solution to the compound inequality -3 ≤ \frac{v}{3} < 3?

Back

Multiply all parts by 3: -9 ≤ v < 9.

Front

How do you solve the inequality 9 ≥ -2m + 2 - 3?

Back

Combine like terms: 9 ≥ -2m - 1; then add 1: 10 ≥ -2m; divide by -2 (reverse the inequality): m ≥ -5.

Front

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

Back

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

Front

What does the inequality m ≤ 5 represent on a number line?

Back

It includes all numbers less than or equal to 5, represented by a closed circle at 5 and shading to the left.

Front

How do you interpret the solution set of an inequality?

Back

The solution set represents all possible values that satisfy the inequality.