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.