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: [beautiful math coming... please be patient] $\displaystyle -\frac{2}{3}x + 6\le 1$
Solution:
Write a nice, clean list of equivalent sentences.
[beautiful math coming... please be patient] $\displaystyle -\frac{2}{3}x + 6\le 1$ (original sentence)
[beautiful math coming... please be patient] $-2x + 18\le 3$ (clear fractions; multiply both sides by $\,3\,$)
[beautiful math coming... please be patient] $-2x \le -15$ (subtract $\,18\,$ from both sides)
[beautiful math coming... please be patient] $\displaystyle x \ge \frac{15}{2}$ (divide both sides by $\,-2\,$; change the direction of the inequality symbol)
Master the ideas from this section
by practicing the exercise at the bottom of this page.

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:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
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AVAILABLE MASTERED IN PROGRESS

Solve: