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 not equal to 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 can be 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 can be either greater than or equal to the value on the right.

Front

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

Back

To solve -4x + 14 ≤ 54, first subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality sign): x ≥ -10.

Front

What is the solution to the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, simplify: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Subtract 18: -14x ≤ 98. Divide by -14 (flip the sign): x ≥ -7.

Front

How do you solve the inequality -3 + x ≤ -11?

Back

Add 3 to both sides: x ≤ -8.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

Distribute: -2x - 4 < 14. Add 4: -2x < 18. Divide by -2 (flip the sign): x > -9.

Front

How do you solve the inequality 6x - 4 ≥ 26?

Back

Add 4 to both sides: 6x ≥ 30. Divide by 6: x ≥ 5.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary value, while non-strict inequalities (≤, ≥) do include the boundary value.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often connected by 'and' or 'or', to describe a range of values.