Solving Two Step Inequalities

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.

Add 4 to both sides: $$-3x < 9$$ . Then divide by -3 (remember to flip the inequality sign): $$x > -3$$ .

The inequality is $$22.50 + x > 32$$ .

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

A filled-in/closed dot is used because the inequality includes the equal sign.

Yes, you flip the sign when dividing or multiplying both sides of an inequality by a negative number.

Subtract 5 from both sides: $$x < 5$$ .

It means that x can take any value greater than 3, represented by an open circle at 3 and shading to the right.

Subtract 6 from both sides: $$-2x > -6$$ . Then divide by -2 (flip the sign): $$x < 3$$ .

You would use a closed dot at 4 and shade to the left, indicating all values less than or equal to 4.