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 solve the inequality -138 ≥ -6(6b − 7)?

Back

First, distribute -6: -138 ≥ -36b + 42. Then, isolate b: -36b ≥ -180, which simplifies to b ≥ 5.

Front

What does the solution b ≥ 5 represent on a number line?

Back

It represents all numbers greater than or equal to 5, including 5 itself, extending to the right on the number line.

Front

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

Back

Distribute -6: -3 - 24x - 36 > -111, then combine like terms.

Front

What is the solution to the inequality x < 3?

Back

It represents all numbers less than 3, extending to the left on the number line.

Front

How do you graph the inequality k < 3?

Back

Draw a number line, place an open circle at 3, and shade to the left to indicate all values less than 3.

Front

What does the inequality 9 ≥ -2m + 2 − 3 simplify to?

Back

It simplifies to 9 ≥ -2m - 1, then to 10 ≥ -2m, leading to m ≥ -5.

Front

What is the significance of an open circle in graphing inequalities?

Back

An open circle indicates that the number is not included in the solution set (e.g., for < or >).

Front

What does the inequality m ≥ -5 represent?

Back

It represents all numbers greater than or equal to -5, including -5 itself, extending to the right on the number line.

Front

What is the process of isolating the variable in an inequality?

Back

It involves performing inverse operations to get the variable alone on one side of the inequality.