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 such as addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations (addition, subtraction, multiplication, division) on both sides of the inequality, just like in equations, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does it mean when an inequality is written as m ≥ -5?

Back

It means that the value of m is greater than or equal to -5, including -5 itself.

Front

Solve the inequality: 9 ≥ -2m + 2 - 3.

Back

m ≥ -5.

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 < 3 indicate in a real-world context?

Back

It indicates that the value of x must be less than 3, which could represent a limit or maximum in a given scenario.

Front

How do you represent a real-world situation as an inequality?

Back

Identify the quantities involved, determine the relationship between them, and express the constraints using inequality symbols.

Front

What is the inequality that models the taxi fare scenario: $2.50 per mile plus a $5 fee, not exceeding $20?

Back

2.50x + 5 ≤ 20.

Front

Solve the equation: (2x - 3) / 4 = 9.

Back

x = 19.5.

Front

What is the significance of the inequality sign in a multistep inequality?

Back

The inequality sign indicates the relationship between two expressions, showing whether one is greater than, less than, or equal to the other.