Solving Linear Inequalities with Integer Coefficients
Need some simpler practice first? Solving Simple Linear Inequalities with Integer Coefficients
Example
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.