Doug C. answered • 12/06/23
Math Tutor with Reputation to make difficult concepts understandable
Solving a linear inequality is very much like solving a linear equation with one exception. When you multiply or divide both sides of an inequality by a negative number the inequality symbol must be reversed.
Notice that is we start with the following true statement:
-3 < 5 and for example multiply both sides by -2 the new result is
6 ? -10 (the expression on the left is now smaller--reverse the arrow to have a true statement. 6 > -10
This happens even if the numbers on either side have the same sign to start:
-2 > -10 , multiply by -1)
2 ? 10 (2 < 10).
In the example problem:
4 - 3x > 16
-3x > 12 (subtract 4 from both sides).
x < 12/(-3) (divide both sides by -3, so reverse the direction of the inequality symbol)
x < -4
Here is a more complicated example:
2(x - 5) - 4(2x +1) < 5x +3
2x - 10 - 8x - 4 < 5x +3 (remove parentheses(
-6x -14 > 5x +3 (combine similar terms)
-6x - 5x > 3 + 14
-11x > 17
x < -17/11
