Solving 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 operations like addition, subtraction, multiplication, or division.

Front

How do you represent a situation where you cannot exceed a certain amount using an inequality?

Back

You can represent it using the 'less than or equal to' (≤) symbol. For example, if you cannot exceed $20, you would write the inequality as x ≤ 20.

Front

What does the inequality 2.50x + 5 ≤ 20 represent in a real-world context?

Back

It represents a scenario where the total taxi fare (2.50 per mile plus a $5 fee) must be less than or equal to $20.

Front

How do you isolate the variable in the inequality 12x + 400 < 1200?

Back

Subtract 400 from both sides to get 12x < 800, then divide by 12 to find x < 66.67.

Front

What is the first step to solve the inequality -3 − 6(4x + 6) > -111?

Back

Distribute -6 to both terms inside the parentheses: -3 - 24x - 36 > -111.

Front

What does the solution x ≥ 2 indicate about the variable x?

Back

It indicates that x can be any number greater than or equal to 2.

Front

How do you check if a solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is the significance of the inequality symbol in 9 ≥ -2m + 2 - 3?

Back

It indicates that the left side (9) is greater than or equal to the right side (-2m + 2 - 3), which helps determine the possible values of m.

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 the difference between < and ≤ in inequalities?

Back

< means 'less than' and does not include the endpoint, while ≤ means 'less than or equal to' and includes the endpoint.