Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

To solve, first 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 6(n + 2) < -72?

Back

First, divide both sides by 6: n + 2 < -12. Then subtract 2: n < -14.

Front

How do you interpret the inequality -2 ≤ x < 5?

Back

This means that x is greater than or equal to -2 and less than 5. The values of x can include -2 but not 5.

Front

What is the solution to the compound inequality -6 < 2t - 5 < 3?

Back

To solve, first add 5 to all parts: -1 < 2t < 8. Then divide by 2: -0.5 < t < 4.

Front

What does the graph of b ≤ -2 look like?

Back

The graph includes a solid dot at -2 and a shaded line extending to the left, indicating all values less than or equal to -2.

Front

What is the difference between 'and' and 'or' in inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

How do you graph the inequality x > 5?

Back

Draw a number line, place an open circle at 5, and shade to the right to indicate all values greater than 5.