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 solve the inequality 77 ≤ 5 + 8n?

Back

First, subtract 5 from both sides: 77 - 5 ≤ 8n, which simplifies to 72 ≤ 8n. Then, divide both sides by 8: 9 ≤ n or n ≥ 9.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be either less than or equal to the value on the right.

Front

Solve 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 is the solution to the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides: 6t ≤ -6. Then, divide by 6: t ≤ -1.

Front

How do you graph the solution of an inequality?

Back

To graph an inequality, draw a number line, place a dot on the number that is the solution, and use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the appropriate side of the number line.

Front

What does the solution k ≥ 7 mean?

Back

The solution k ≥ 7 means that k can be any number greater than or equal to 7.

Front

Solve the inequality -8k - 4 ≤ -60.

Back

Add 4 to both sides: -8k ≤ -56. Then, divide by -8 (flip the inequality): k ≥ 7.

Front

What is the solution to the inequality 0 ≥ -5x - 5?

Back

Add 5 to both sides: 5 ≥ -5x. Then, divide by -5 (flip the inequality): x ≥ -1.

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 adding or subtracting a constant from both sides.