Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Front

How do you represent 'no more than' in an inequality?

Back

'No more than' is represented as ≤ (less than or equal to). For example, 'no more than 18 students' is written as s ≤ 18.

Front

How do you represent 'at least' in an inequality?

Back

'At least' is represented as ≥ (greater than or equal to). For example, 'at least 25 cats' is written as c ≥ 25.

Front

What does the inequality 5 + x ≥ 29 mean?

Back

It means that when you add 5 to x, the result is greater than or equal to 29.

Front

How do you solve the inequality 77 ≤ 5 + 8n?

Back

To solve, subtract 5 from both sides: 72 ≤ 8n, then divide by 8: 9 ≤ n or n ≥ 9.

Front

What is the solution to the inequality g ≤ 45?

Back

The solution indicates that g can be any value less than or equal to 45.

Front

What does the graph of x < 3 look like?

Back

The graph shows an open circle at 3 and a line extending to the left, indicating all values less than 3.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by performing the opposite operation (addition or subtraction).

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.

Front

How do you graph the solution of n ≥ 9?

Back

You place a closed circle on 9 and shade to the right, indicating all values greater than or equal to 9.