{ Lesson 5.05 Module 5 Activity

 Solve the equation  Solve the equation –x + 3 > 7. The first step in solving this inequality is to “isolate” the variable. To do so, you need to to subtract 3 from 7.  Now that you have –x > 4, you need to move the negative sign to the right side of the equation. Do you know how to do this?  We now have an inequality of –x > 4. Now that you have –x > 4, you need to move the negative sign to the right side of the equation. Do you know how to do this?   To move the negative sign in the inequality –x > 4 to the right side of the inequality, you need to treat it as though the equation is x(-1) > 4. Now, all you need to do is divide 4 by -1, or just “-”. This gives you the inequality of x > -4. There’s just one more step needed to finish the equation. Whenever you are multiplying or dividing by a negative number in an inequality, you always switch the inequality symbol.   Your final answer is: X < -4 Go to the next page to find out why you always switch the inequality symbol!

  When you multiply or divide any non-zero number by a negative, it’s sign changes. If it was positive it becomes negative and if it was negative it becomes positive. On a number line, the number "flips" over to the other side of zero. When you multiply or divide both sides of an inequality this happens to both numbers, the one on the "less than" side and the one on the "greater than" side. Both sides "flip". When this happens, the number that was on the left side is now to the right side. In other words, what was less than before is now greater than. (And the number that was to the right (i.e. greater than) ends up to the left of (or less than) the other number.) This is why we have to reverse ("flip") the inequality whenever we multiply or divide it by a negative number. Why do you need to “flip” the inequality symbol when multiplying or dividing by a negative number?

 Look at the equation -2x * Don’t forget to switch the inequality sign. *  Look at the equation -4x – 8 > 16. The first step in solving this inequality is to add 8 to 16. This gives you an inequality of -4x > 24. The final step in this inequality is to divide 24 by -4. This gives you an inequality of x 16. The first step in solving this inequality is to add 8 to 16. This gives you an inequality of -4x > 24. The final step in this inequality is to divide 24 by -4. This gives you an inequality of x < -6. Lets look at some more examples.