Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≤' mean?

Back

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

Front

What does the symbol '≥' mean?

Back

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

Front

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

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the solution to the inequality 5w ≥ 30?

Back

Divide both sides by 5: w ≥ 6.

Front

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

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

What is the first step in solving the inequality 6 + 2h > 30?

Back

Subtract 6 from both sides: 2h > 24.

Front

What is the solution to the inequality 30x + 600 ≥ 1500?

Back

Subtract 600 from both sides: 30x ≥ 900. Then divide by 30: x ≥ 30.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting in a contradiction.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, such as a < x < b.