Solving 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 typically involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -4x - 7 ≥ 21?

Back

Add 7 to both sides: -4x ≥ 28. Then divide by -4 (remember to flip the inequality): x ≤ -7.

Front

What is the solution to the inequality 7b - 3 < 11?

Back

Add 3 to both sides: 7b < 14. Then divide by 7: b < 2.

Front

How do you solve the inequality -2(x + 2) < 14?

Back

Distribute -2: -2x - 4 < 14. Add 4 to both sides: -2x < 18. Then divide by -2 (flip the inequality): x > -9.

Front

What is the solution to the inequality 6 + 2h > 30?

Back

Subtract 6 from both sides: 2h > 24. Then divide by 2: h > 12.

Front

How do you 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 does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

What is the difference between 'greater than' and 'less than' inequalities?

Back

'Greater than' (>) indicates that one value is larger than another, while 'less than' (<) indicates that one value is smaller than another.

Front

What is the graphical representation of an inequality?

Back

An inequality can be represented on a number line with an open circle for 'greater than' or 'less than' and a closed circle for 'greater than or equal to' or 'less than or equal to'.

Front

What is a solution set in the context of inequalities?

Back

A solution set is the set of all values that satisfy the inequality.