Solving Inequalities

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' represents 'less than'.

Front

How do you solve the inequality 8x ≥ -32?

Back

To solve 8x ≥ -32, divide both sides by 8, resulting in x ≥ -4.

Front

What is the solution to the inequality 11x + 16 < 43 + 2x?

Back

The solution is x < 3.

Front

What does it mean when an inequality states x ≥ 1?

Back

It means that x is greater than or equal to 1.

Front

In the inequality 5 ≥ x, will the dot be colored in at x = 5?

Back

Yes, the dot will be colored in because 5 is included in the solution.

Front

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

Back

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

Front

How do you graph the inequality x < 2 on a number line?

Back

You draw an open circle at 2 and shade to the left to indicate all numbers less than 2.

Front

What does the solution set of an inequality represent?

Back

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

Front

How do you solve the compound inequality 1 < x ≤ 4?

Back

The solution is all x values that are greater than 1 and less than or equal to 4.

Front

What is the significance of the boundary point in an inequality?

Back

The boundary point indicates the value at which the inequality changes from true to false.