Solving Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to'.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'.

Front

How do you solve the inequality 4 - 7y ≤ 18?

Back

Subtract 4 from both sides to get -7y ≤ 14, then divide by -7 (remember to flip the inequality sign) to find y ≥ -2.

Front

What is the solution to the inequality 16 - 4a > 8?

Back

Subtract 16 from both sides to get -4a > -8, then divide by -4 to find a < 2.

Front

How do you isolate the variable in the inequality 14x + 12 < 9x - 3?

Back

Subtract 9x from both sides to get 5x + 12 < -3, then subtract 12 from both sides to find 5x < -15, and finally divide by 5 to get x > -3.

Front

What is the solution to the inequality 14 + 9x > 6x + 4?

Back

Subtract 6x from both sides to get 14 + 3x > 4, then subtract 14 from both sides to find 3x > -10, and finally divide by 3 to get x > -3 1/3.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality.

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities, often using 'and' or 'or'.