Examples of multiplying of dividing both sides of an inequality by a negative number. Example 1 Solve         1 - 3x  >  16 Solution We use the two step method.  We see that x is multiplied by -3 and then a 1 is added.  We undo these operations using the 2-step method. Step 1:  Subtract 1 from both sides         1 - 3x  >  16       - 1            - 1 -------------------------             -3x  >  15 Step 2:  Divide both sides by -3.  Since -3 is a negative number, we must switch the order of the inequality sign when we divide.         -3x  <  15        ----      ----         -3        -3         x  <  -5   Now try one by yourself.  If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear. Exercise 1 Solve         2 - 5x  <  37 Answer         Example 2 Solve         -x/2 - 6 >  17 Solution We use the two step method.  We see that x is divided by -2 and then 6 is subtracted.  We undo these operations using the 2-step method. Step 1:  Add 6 to both sides         -x/2 - 6 >  17               + 6   + 6 -------------------------             -x/2  >  23 Step 2:  Multiply both sides by -2.  Since -2 is a negative number, we must switch the order of the inequality sign when we divide.         (-2)(-x/2)  <  (-2)(23)           x  <  -46   Now try one by yourself.  If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear. Exercise 2 Solve         -x/4 + 3  <  -8 Answer         Back to the supplement on 2-step equations and inequalities