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 (≤) to indicate that the total must not exceed the specified amount.

Front

What does the inequality 12x + 400 < 1200 represent in a real-world context?

Back

It represents a scenario where after making a $400 down payment, the total monthly payments (12 months at x dollars each) must be less than $1200.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What is the solution to the inequality 9 ≥ -2m + 2 - 3?

Back

The solution is m ≥ -5.

Front

What does the inequality 2.50x + 5 ≤ 20 model?

Back

It models a situation where the total taxi fare, which is $2.50 per mile plus a $5 fee, must not exceed $20.

Front

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

Back

The first step is to distribute -6 to both terms inside the parentheses: -3 - 24x - 36 > -111.

Front

What does it mean when an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality, often resulting in a contradiction.

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 makes the inequality true.

Front

What is the difference between < and ≤ in inequalities?

Back

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