Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

What does the symbol '<' mean in inequalities?

Back

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

Front

What does the symbol '>' mean in inequalities?

Back

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

Front

What does the symbol '≤' mean in inequalities?

Back

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

Front

What does the symbol '≥' mean in inequalities?

Back

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

Front

How do you solve the compound inequality -13 < 2x + 5 < 15?

Back

First, isolate 2x: -18 < 2x < 10. Then divide by 2: -9 < x < 5.

Front

What is the solution set for the inequality 2x + 1 > 9 or x - 4 < 6?

Back

The solution set is all real numbers, since both inequalities can be satisfied by various values of x.

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How do you express the solution for the inequality -2 ≤ x ≤ 5?

Back

The solution can be expressed as the interval [-2, 5], which includes both endpoints.

Front

What is the solution for the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

The solution is x ≥ -5 and x < 4.

Front

What is the solution for the inequality 3x + 2 < -7 or -4x + 5 < 1?

Back

The solution is x < -3 or x > 1.