Solving Inequalities

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 an inequality?

Back

'≥' means 'greater than or equal to'.

Front

How do you solve the inequality 0.75m + 1.75 ≤ 20 for m?

Back

Subtract 1.75 from both sides to get 0.75m ≤ 18.25, then divide by 0.75 to find m ≤ 24.33.

Front

What is the first step in solving the inequality 10.25h ≥ 550?

Back

Divide both sides by 10.25 to isolate h.

Front

What does it mean to 'flip' the inequality symbol?

Back

Flipping the inequality symbol means changing '>' to '<' or '≥' to '≤' when multiplying or dividing both sides of an inequality by a negative number.

Front

What is the solution to the inequality 5w ≥ 30?

Back

w ≥ 6.

Front

How can you represent the solution to an inequality on a number line?

Back

Use an open circle for '>' or '<' and a closed circle for '≥' or '≤', and shade the appropriate direction.

Front

What is the importance of rounding up when solving application-based inequalities?

Back

Rounding up ensures that you account for whole units in real-life scenarios, such as hours worked or items purchased.

Front

What is the general form of a linear inequality?

Back

A linear inequality can be expressed in the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.

Front

What does the term 'additional miles' refer to in the context of the taxi cab problem?

Back

'Additional miles' refers to the distance traveled beyond the initial fare included in the taxi cost.