Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does the symbol '≥' mean in an inequality?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

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

Front

How do you solve the inequality -7 + 10z > -27?

Back

Add 7 to both sides: 10z > -20. Then divide by 10: z > -2.

Front

What is the solution to the inequality 5(v + 3) - 10v > -10?

Back

Distribute and simplify: 5v + 15 - 10v > -10. Combine like terms: -5v + 15 > -10. Subtract 15: -5v > -25. Divide by -5 (reverse the inequality): v < 5.

Front

What does an open circle on a number line represent?

Back

An open circle represents that the number is not included in the solution set, typically used with < or >.

Front

What does a closed circle on a number line represent?

Back

A closed circle represents that the number is included in the solution set, typically used with ≤ or ≥.

Front

How do you graph the inequality x < 4?

Back

Draw a number line, place an open circle at 4, and shade to the left to indicate all numbers less than 4.