SOLVING LINEAR INEQUALITIES INVOLVING FRACTIONS

Remember: If you multiply or divide both sides of an inequality by a negative number,
then you must change the direction of the inequality symbol.

EXAMPLE:
Solve: $\displaystyle -\frac{2}{3}x + 6\le 1$
Solution:
Write a nice, clean list of equivalent sentences.
 $\displaystyle -\frac{2}{3}x + 6\le 1$ (original sentence) $-2x + 18\le 3$ (clear fractions; multiply both sides by $\,3\,$) $-2x \le -15$ (subtract $\,18\,$ from both sides) $\displaystyle x \ge \frac{15}{2}$ (divide both sides by $\,-2\,$; change the direction of the inequality symbol)
Master the ideas from this section

When you're done practicing, move on to:
Solving Linear Inequalities, All Mixed Up

Solve the given inequality.
Write the result in the most conventional way.

For more advanced students, a graph is displayed.
For example, the inequality $-\frac{2}{3}x + 6\le 1$
is optionally accompanied by the graph of $\,y = -\frac{2}{3}x + 6\,$ (the left side of the inequality, dashed green)
and the graph of $\,y = 1\,$ (the right side of the inequality, solid purple).
In this example, you are finding the values of $\,x\,$ where the green graph lies on or below the purple graph.
Click the “show/hide graph” button if you prefer not to see the graph.

CONCEPT QUESTIONS EXERCISE: