Front

What does a closed dot on a number line indicate?

Back

A closed dot indicates that the number is included in the solution set (e.g., for the inequality 5 ≥ x, x can equal 5).

Front

How do you solve the system of equations: x=4 and 2x+3y=-4?

Back

Substituting x=4 into the second equation gives 2(4)+3y=-4, which simplifies to 8+3y=-4. Solving for y gives y=-4. The solution is (4, -4).

Front

What does the inequality x ≤ 10.5 mean?

Back

It means that x can take any value less than or equal to 10.5.

Front

How can you represent the inequality 2 > p on a number line?

Back

It can be represented as a number line with an open dot at 2 and shading to the left, indicating all values less than 2.

Front

What does the inequality x ≥ 3 signify?

Back

It signifies that x can take any value greater than or equal to 3.

Front

What is the difference between x > 3 and x ≥ 3?

Back

x > 3 means x can be any value greater than 3 (not including 3), while x ≥ 3 includes 3 as well.

Front

What does the term 'inequality' refer to in mathematics?

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

How do you graph the inequality x < 5?

Back

You draw a number line, place an open dot at 5, and shade to the left to indicate all values less than 5.

Front

What is the solution set for the inequality 3x - 2 < 7?

Back

To solve, add 2 to both sides: 3x < 9. Then divide by 3: x < 3. The solution set is all x values less than 3.

Front

What does the term 'solution set' mean?

Back

The solution set is the set of all values that satisfy a given inequality or equation.