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

The symbol '>' means 'greater than'.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality -4(-7-5x) > 188?

Back

First, distribute -4 to get 28 + 20x > 188. Then, subtract 28 from both sides to get 20x > 160. Finally, divide by 20 to find x > 8.

Front

What is the solution to the inequality -9e - 8 + 4e ≤ -1?

Back

Combine like terms to get -5e - 8 ≤ -1. Add 8 to both sides to get -5e ≤ 7. Divide by -5 (remember to flip the inequality) to find e ≥ -1⅖.

Front

How do you solve the inequality -138 ≥ -6(6b - 7)?

Back

Distribute -6 to get -138 ≥ -36b + 42. Subtract 42 from both sides to get -180 ≥ -36b. Divide by -36 (remember to flip the inequality) to find b ≥ 5.

Front

What is the solution to the inequality 3(d + 2) < -15?

Back

Distribute 3 to get 3d + 6 < -15. Subtract 6 from both sides to get 3d < -21. Divide by 3 to find d < -7.

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.