Solving Linear Inequalities with Integer Coefficients

EXAMPLE:

Solve:

$3 - 2x \le 5x + 1$

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.

$3 - 2x \le 5x + 1$	(original sentence)
$3 - 7x \le 1$	(subtract $\,5x\,$ from both sides)
$-7x \le -2$	(subtract $\,3\,$ from both sides)
$x \ge \frac{2}{7}$	(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

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.