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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.8.EE.C.7A

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.

Tags

CCSS.6.EE.B.5

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.

Tags

CCSS.6.EE.B.8