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

How do you solve the inequality 6 + 2h > 30?

Back

To solve for h, subtract 6 from both sides to get 2h > 24, then divide by 2 to find h > 12.

Front

What does the inequality x + 5 > 7 represent?

Back

It represents that x must be greater than 2, as you can solve it by subtracting 5 from both sides.

Front

How can you represent the solution to the inequality 5w ≥ 30 on a number line?

Back

You would shade to the right of 6 on the number line, indicating that w can be 6 or any number greater than 6.

Front

What is the first step in solving the inequality 30x + 600 ≥ 1,500?

Back

Subtract 600 from both sides to isolate the term with x, resulting in 30x ≥ 900.

Front

What does the solution x < -4 indicate on a number line?

Back

It indicates that all numbers to the left of -4, not including -4 itself, are solutions to the inequality.

Front

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

Back

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

Front

How do you graph the solution to an inequality like x > 2?

Back

You would draw an open circle at 2 and shade to the right, indicating that 2 is not included in the solution.

Front

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

Back

The boundary point is the value that separates the solutions from non-solutions; whether it is included depends on whether the inequality is strict or non-strict.

Front

How do you check if a solution to an inequality is correct?

Back

You can substitute the solution back into the original inequality to see if it makes the inequality true.