Two-Step Inequalities

A two-step inequality is an inequality that requires two operations to isolate the variable on one side of the inequality sign.

Subtract 2 from both sides to get 3x > 12, then divide by 3 to find x > 4.

Add 4 to both sides to get 4x > 12, then divide by 4 to find x > 3.

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -1.

Subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (remember to flip the inequality) to find x ≥ -10.

Subtract 7 from both sides to get -2x < 12, then divide by -2 (remember to flip the inequality) to find x > -6.

When you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality sign.

The first step is usually to isolate the term with the variable by performing the inverse operation (addition or subtraction) on both sides.

Yes, some two-step inequalities can have no solution, such as when the variable cancels out and results in a false statement.

The graphical representation of an inequality shows a number line with an open or closed circle at the boundary point and shading to indicate the solution set.