2-step Inequalities

Front

What is a 2-step inequality?

Back

A 2-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -9a - 1 < 26?

Back

Add 1 to both sides: -9a < 27. Then divide by -9 (remember to flip the inequality): a > -3.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

The inequality symbol flips direction.

Front

Solve for k: 7k - 2 ≥ -9.

Back

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

Front

Solve the inequality -4x + 5 ≤ 29.

Back

Subtract 5 from both sides: -4x ≤ 24. Then divide by -4 (flip the inequality): x ≥ -6.

Front

Solve the inequality -4x + 14 ≤ 54.

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (flip the inequality): x ≥ -10.

Front

What is the solution set for the inequality x + 3 > 5?

Back

x > 2.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that satisfy the inequality, often resulting in a contradiction.

Front

What is the graphical representation of an inequality?

Back

An inequality is represented on a number line with an open or closed circle and a shaded region indicating the solution set.