SOLVING LINEAR INEQUALITIES WITH INTEGER COEFFICIENTS
EXAMPLE:
Solve: [beautiful math coming... please be patient] $3 - 2x \le 5x + 1$
Solution: Solution:
Write a nice, clean list of equivalent sentences.
Remember that whenever you multiply or divide both sides of an inequality by a negative number,
then you must change the direction of the inequality symbol.
[beautiful math coming... please be patient] $3 - 2x \le 5x + 1$ (original sentence)
[beautiful math coming... please be patient] $3 - 7x \le 1$ (subtract $\,5x\,$ from both sides)
[beautiful math coming... please be patient] $-7x \le -2$ (subtract $\,3\,$ from both sides)
[beautiful math coming... please be patient] $x \ge \frac{2}{7}$ (divide both sides by $\,-7\,$; 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 Involving Fractions

 
 

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

For more advanced students, a graph is displayed.
For example, the inequality $3 - 2x \le 5x + 1$
is optionally accompanied by the graph of $\,y = 3 - 2x\,$ (the left side of the inequality, dashed green)
and the graph of $\,y = 5x + 1\,$ (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:
1 2 3 4 5 6
AVAILABLE MASTERED IN PROGRESS

Solve: