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

        x > -7

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

        x >= 44

Back to the supplement on 2-step equations and inequalities