Solving Linear Inequalities

Task goals

• Solve a two-step linear inequality such as $3x+2>14$ by undoing the operations in reverse order, in the same way as an equation.
• Flip the inequality sign when multiplying or dividing both sides by a negative number, such as solving $-2x>10$ to get $x<-5$.
• Read a solution set from a number line, using an open circle for a strict inequality and a filled circle for an inclusive one, and write it in inequality notation.
• Represent the solution set of an inequality on a number line, choosing an open or filled circle and the correct ray direction.
• Solve a compound (double) inequality such as $-3<2x+1\le7$ by applying the same operation to all three parts at once.
• Identify and correct a common error, such as forgetting to flip the sign on a negative step, or forgetting to apply a step to all three parts of a compound inequality.