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 often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 11 > -3y + 2?

Back

First, subtract 2 from both sides: 11 - 2 > -3y. Then, simplify: 9 > -3y. Next, divide by -3 (remember to flip the inequality): -3 < y.

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

Solve for k: 7k – 2 ≥ -9

Back

Add 2 to both sides: 7k ≥ -7. Then divide by 7: k ≥ -1.

Front

What is the solution to the inequality -4x + 1 > 21?

Back

Subtract 1 from both sides: -4x > 20. Then divide by -4 (flip the sign): x < -5.

Front

How do you isolate the variable in the inequality 2x + 6 ≥ -8?

Back

Subtract 6 from both sides: 2x ≥ -14. Then divide by 2: x ≥ -7.

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is strictly more than another, while 'greater than or equal to' (≥) includes the possibility of being equal.

Front

What does the solution x < -5 represent on a number line?

Back

It represents all numbers to the left of -5, not including -5 itself.

Front

How do you check the solution of an inequality?

Back

Substitute a value from the solution set back into the original inequality to see if it holds true.