# 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.