Solve Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, or ≥) to show that one expression is larger or smaller than the other.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (remember to flip the inequality sign): x ≥ -10.

Front

What does it mean when an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality. For example, if you have an inequality that simplifies to a false statement like 0 < -1.

Front

What is the solution to the inequality 8(m + 2) < 4(5 + 2m)?

Back

All real numbers, because the inequality simplifies to a true statement.

Front

How do you solve the inequality 6t + 4 ≤ -2?

Back

1. Subtract 4 from both sides: 6t ≤ -6. 2. Divide by 6: t ≤ -1.

Front

When solving inequalities, do you flip the inequality sign when multiplying or dividing by a negative number?

Back

Yes, you must flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

1. Add 9 to both sides: 2k ≤ -10. 2. Divide by 2: k ≤ -5.

Front

What does it mean if an inequality is true for all real numbers?

Back

It means that any value you substitute into the inequality will make it true.

Front

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

Back

Strict inequalities use < or >, while non-strict inequalities use ≤ or ≥, allowing for equality.

Front

How do you graph the solution of an inequality on a number line?

Back

Use an open circle for strict inequalities (< or >) and a closed circle for non-strict inequalities (≤ or ≥). Shade the region that represents the solution.