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 < 11, you would first subtract 3 and then divide by 2.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you solve the inequality 16 - 4a > 8?

Back

First, subtract 16 from both sides: -4a > -8. Then, divide by -4 (remember to flip the inequality): a < 2.

Front

How do you solve the inequality -7x + 1 ≤ 22?

Back

First, subtract 1 from both sides: -7x ≤ 21. Then, divide by -7 (flip the inequality): x ≥ -3.

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

How do you graph the inequality 6 > x?

Back

You would graph a number line, place an open circle at 6, and shade to the left to indicate all numbers less than 6.

Front

What is the solution set for the inequality a ≥ 11?

Back

The solution set includes all numbers greater than or equal to 11.