﻿ Solving Linear Inequalities with Integer Coefficients
SOLVING LINEAR INEQUALITIES WITH INTEGER COEFFICIENTS
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)
• An example is given below.
Want more details, more exercises?
• Need some simpler practice first?

EXAMPLE:
Solve: $3 - 2x \le 5x + 1$
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

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: