# Solving Linear Inequalities with Integer Coefficients

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

## Concept Practice

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

For more advanced students, a graph is available. 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 to toggle the graph.

Solve: