Inequalities Review!

Front

What does the inequality x > -4 represent on a number line?

Back

It represents all numbers greater than -4, with an open circle at -4 indicating that -4 is not included.

Front

How do you solve the inequality 7k - 2 ≥ -9 for k?

Back

Add 2 to both sides to get 7k ≥ -7, then divide by 7 to find k ≥ -1.

Front

What is the difference between an open circle and a closed circle on a number line?

Back

An open circle indicates that the number is not included in the solution (e.g., x < 5), while a closed circle indicates that the number is included (e.g., x ≤ 5).

Front

When graphing the inequality b < 6, what type of circle is used?

Back

An open circle is used to indicate that 6 is not included in the solution.

Front

What is the solution set for the inequality x ≤ 3?

Back

The solution set includes all numbers less than or equal to 3.

Front

How do you graph the inequality y > 2 on a coordinate plane?

Back

Draw a dashed horizontal line at y = 2 and shade the area above the line.

Front

What does the inequality 3x + 4 < 10 mean?

Back

It means that the expression 3x + 4 is less than 10, which can be solved to find the values of x that satisfy this condition.

Front

How do you solve the compound inequality -2 < x + 3 < 5?

Back

Subtract 3 from all parts to get -5 < x < 2.

Front

What is the graphical representation of the inequality x ≥ 0?

Back

It is represented by a closed circle at 0 and a line extending to the right.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that satisfy the inequality, often resulting from contradictory statements.