Two Step Inequalities - Graphing

Front

What is a two-step inequality?

Back

An inequality that requires two operations to isolate the variable, often involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What does the solution n > 11 look like on a number line?

Back

An open circle at 11 with a line extending to the right.

Front

What is the difference between an open circle and a closed circle on a graph?

Back

An open circle indicates that the number is not included (e.g., < or >), while a closed circle indicates that the number is included (e.g., ≤ or ≥).

Front

How do you graph the inequality b < 6?

Back

Use an open circle at 6 and shade to the left.

Front

What is the solution to the inequality 2 - 3x ≤ 20?

Back

x ≥ -6.

Front

How do you isolate x in the inequality 2 - 3x ≤ 20?

Back

Subtract 2 from both sides: -3x ≤ 18, then divide by -3 (remember to flip the inequality): x ≥ -6.

Front

What does the inequality 6 > x mean?

Back

It means x is less than 6.

Front

How do you represent the solution x < 6 on a number line?

Back

An open circle at 6 with a line extending to the left.

Front

What is the first step in solving the inequality 5x + 3 < 18?

Back

Subtract 3 from both sides: 5x < 15.