Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality -p - 4p > -10?

Back

Combine like terms: -5p > -10. Then divide by -5 (remember to flip the inequality): p < 2.

Front

What does the inequality symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to another value.

Front

How do you solve the inequality 28 - k ≥ 7(k - 4)?

Back

Distribute: 28 - k ≥ 7k - 28. Combine like terms: 56 ≥ 8k. Divide by 8: k ≤ 7.

Front

What is the solution to the inequality 3 < -5n + 2n?

Back

Combine like terms: 3 < -3n. Divide by -3 (flip the inequality): n < -1.

Front

How do you solve the inequality 6x + 2 < 14?

Back

Subtract 2: 6x < 12. Divide by 6: x < 2.

Front

What does the inequality symbol '<' mean?

Back

The symbol '<' means 'less than', indicating that one value is smaller than another.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

Distribute: -3 - 24x - 36 > -111. Combine like terms: -24x > -72. Divide by -24 (flip the inequality): x < 3.

Front

What is the importance of flipping the inequality sign when 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 is a solution set in the context of inequalities?

Back

A solution set is the set of all values that satisfy the inequality.