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 (>, <, ≥, ≤) instead of an equal sign.

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 can be less than or equal to the value on the right.

Front

How do you solve the inequality: 2(x + 1) ≤ 3x - 4?

Back

First, distribute: 2x + 2 ≤ 3x - 4. Then, subtract 2x from both sides: 2 ≤ x - 4. Finally, add 4 to both sides: x ≥ 6.

Front

What is the solution set for the inequality: 4x - 7 > 5x + 3?

Back

The solution set is x < -10.

Front

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

Back

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

Front

How do you solve the inequality: 3x + 2 > 5x - 4?

Back

First, subtract 3x from both sides: 2 > 2x - 4. Then, add 4 to both sides: 6 > 2x. Finally, divide by 2: 3 > x or x < 3.

Front

What is the solution set for the inequality: 2(3x - 1) ≤ 4x + 5?

Back

The solution set is x ≤ 3.5.

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 can be greater than or equal to the value on the right.

Front

How do you solve the inequality: -7x + 15 ≥ -20?

Back

First, subtract 15 from both sides: -7x ≥ -35. Then, divide by -7 (remember to flip the inequality): x ≤ 5.

Front

What is the solution set for the inequality: x + 4 < 10?

Back

The solution set is x < 6.