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 not equal to the other.

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

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

How do you solve the inequality 3.6 - 4.85a ≥ -6.1?

Back

To solve, isolate 'a': 3.6 + 6.1 ≥ 4.85a, which simplifies to 9.7 ≥ 4.85a, then divide by 4.85 to get a ≤ 2.

Front

What is the solution to the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

How do you graph the inequality x ≤ 8?

Back

On a number line, draw a closed dot at 8 and shade to the left to indicate all numbers less than or equal to 8.

Front

What does the inequality 14 < -2a + 6 - 2a represent?

Back

It represents a condition where the expression on the right is less than 14. Solving gives a < -2.

Front

When do you use an open dot on a graph of an inequality?

Back

An open dot is used for inequalities with < or >, indicating that the endpoint is not included in the solution.

Front

What does the statement '7 is less than a number' translate to in inequality form?

Back

It translates to x > 7.

Front

What is the solution to the inequality -3x + 4 < 10?

Back

Subtract 4 from both sides: -3x < 6, then divide by -3 (remember to flip the inequality): x > -2.