Representing, Solving, Explaining, and Interpreting 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'. It indicates that one value is either less than or equal to another.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that one value is either greater than or equal to another.

Front

How do you solve the inequality: 2(4x - 3) ≤ 10?

Back

First, distribute: 8x - 6 ≤ 10. Then, add 6 to both sides: 8x ≤ 16. Finally, divide by 8: x ≤ 2.

Front

What is the solution to the inequality: 3n + 3 ≥ 30?

Back

Subtract 3 from both sides: 3n ≥ 27. Then, divide by 3: n ≥ 9.

Front

How do you represent the solution x > 10 on a number line?

Back

Use an open circle at 10 and shade to the right to indicate all numbers greater than 10.

Front

What is the solution to the inequality: -8x + 7 < 15?

Back

Subtract 7 from both sides: -8x < 8. Then, divide by -8 (remember to flip the inequality): x > -1.

Front

How do you graph the solution x ≥ -5?

Back

Use a closed circle at -5 and shade to the right to indicate all numbers greater than or equal to -5.

Front

What is the difference between an open circle and a closed circle on a graph?

Back

An open circle indicates that the number is not included in the solution (e.g., < or >), while a closed circle indicates that the number is included (e.g., ≤ or ≥).

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality by performing inverse operations.