Sec. 4-4 PI Solve and Graph 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. For example, in the inequality 2x + 3 > 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality 6c + 4 > 22?

Back

First, subtract 4 from both sides: 6c > 18. Then, divide by 6: c > 3.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves drawing a number line and indicating the solution set. A closed circle indicates that the number is included (≤ or ≥), while an open circle indicates it is not included (< or >).

Front

What is the solution to the inequality 77 ≤ 5 + 8n?

Back

First, subtract 5 from both sides: 72 ≤ 8n. Then, divide by 8: 9 ≤ n or n ≥ 9.

Front

What does a closed circle on a graph represent?

Back

A closed circle on a graph indicates that the endpoint is included in the solution set, meaning the value satisfies the inequality (e.g., ≤ or ≥).

Front

What does an open circle on a graph represent?

Back

An open circle on a graph indicates that the endpoint is not included in the solution set, meaning the value does not satisfy the inequality (e.g., < or >).

Front

How do you solve the inequality 2k - 9 ≤ -19?

Back

First, add 9 to both sides: 2k ≤ -10. Then, divide by 2: k ≤ -5.

Front

What is the solution to the inequality 7n - 1 > 76?

Back

First, add 1 to both sides: 7n > 77. Then, divide by 7: n > 11.

Front

What is the difference between ≤ and < in inequalities?

Back

The symbol ≤ means 'less than or equal to,' including the endpoint, while < means 'less than,' excluding the endpoint.

Front

What is the first step in solving the inequality 2x + 5 < 15?

Back

Subtract 5 from both sides: 2x < 10.