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

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'.

Front

What does the symbol '≥' represent in inequalities?

Back

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

Front

What does the symbol '≤' represent in inequalities?

Back

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

Front

How do you solve the inequality 3x + 15 ≤ 21?

Back

To solve the inequality, subtract 15 from both sides to get 3x ≤ 6, then divide by 3 to find x ≤ 2.

Front

How do you solve the inequality 5(k + 8) - 7 ≤ 23?

Back

First, distribute 5 to get 5k + 40 - 7 ≤ 23. Then simplify to 5k + 33 ≤ 23, subtract 33 from both sides to get 5k ≤ -10, and finally divide by 5 to find k ≤ -2.

Front

How do you solve the inequality 2p + 5 ≥ 3p - 10?

Back

First, subtract 2p from both sides to get 5 ≥ p - 10. Then add 10 to both sides to find 15 ≥ p, or p ≤ 15.

Front

What is the solution set for the inequality x ≥ 0?

Back

The solution set is all real numbers x such that x is greater than or equal to 0, which can be represented as [0, ∞).

Front

What is the graphical representation of the inequality x < 3?

Back

The graphical representation is a number line with an open circle at 3 and a line extending to the left, indicating all numbers less than 3.