Solving Inequalities (Friedman)

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 in an inequality?

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 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 2(x − 4) < 26?

Back

First, distribute: 2x - 8 < 26. Then, add 8 to both sides: 2x < 34. Finally, divide by 2: x < 17.

Front

What is the solution to the inequality 3(x + 5) + 3 ≥ 30?

Back

First, simplify: 3x + 15 + 3 ≥ 30. Then, combine like terms: 3x + 18 ≥ 30. Subtract 18: 3x ≥ 12. Finally, divide by 3: x ≥ 4.

Front

What does the solution 'n < 11' mean in the context of the inequality 2n - 6 < 16?

Back

It means that any value of n that is less than 11 will satisfy the inequality.

Front

How do you interpret the solution x < 7 from the inequality 3x - 5 < 16?

Back

It means that any value of x that is less than 7 will satisfy the inequality.

Front

What is the solution to the inequality 2(3x + 4) + 5 > 55?

Back

First, simplify: 6x + 8 + 5 > 55. Combine like terms: 6x + 13 > 55. Subtract 13: 6x > 42. Finally, divide by 6: x > 7.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only.

Front

What is the difference between '≥' and '>'?

Back

'≥' means 'greater than or equal to', while '>' means 'greater than' only.