This one is a role reversal!
Up to this point, students have been exposed to expressing basic real world problems with inequalities using only positive coefficients. The activity Solve and Graph Two-Step Inequalities is the first opportunity for students to use negative coefficients with inequalities.
The activity begins by using a number line to show students that when they multiply or divide by a positive number the inequality remains true. This is followed by a review of the similarities between solving an equation and solving an inequality, using only positive numbers. Now students are ready to move to multiplying and dividing by a negative number. Again, the use of a number line shows that multiplying or dividing by a negative number causes the inequality to reverse for the expression to remain true.
Once students have mastered these skills, they solve two-step inequalities, translate between word problems and symbols, show solutions visually on a number line, and interpret their solutions verbally. This activity is a great preparation for inequalities they will encounter in the future.