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, or not equal to the other.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality 10 ≥ x - 3?

Back

Add 3 to both sides to get 13 ≥ x, which can be rewritten as x ≤ 13.

Front

What is the solution to the inequality 5z - 2 - 2z < 13?

Back

Combine like terms to get 3z - 2 < 13, then add 2 to both sides to get 3z < 15, and finally divide by 3 to find z < 5.

Front

What does the number line graph representing x ≥ -5 look like?

Back

The graph includes a closed dot at -5 and a line extending to the right, indicating all numbers greater than or equal to -5.

Front

How do you solve the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute to get 3x - 6 < 2x + 18, then subtract 2x from both sides to get x - 6 < 18, and finally add 6 to both sides to find x < 24.

Front

What is the solution to the inequality 7(x + 3) < 5x + 13?

Back

Distribute to get 7x + 21 < 5x + 13, then subtract 5x from both sides to get 2x + 21 < 13, and finally subtract 21 to find 2x < -8, leading to x < -4.

Front

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

Back

Strict inequalities use '>' or '<' and do not include the endpoint, while non-strict inequalities use '≥' or '≤' and include the endpoint.

Front

How can you check the solution of an inequality?

Back

You can check the solution by substituting a value from the solution set back into the original inequality to see if it holds true.