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audio read-through Solving Linear Inequalities with Integer Coefficients

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

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
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Master the ideas from this section by practicing below:

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When you're done practicing, move on to:

Solving Linear Inequalities Involving Fractions
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Concept Practice

  1. Choose a specific problem type, or click ‘New problem’ for a random question.
  2. Think about your answer.
  3. Click ‘Check your answer’ to check!

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.

PROBLEM TYPES:
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6
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Solve:
To get a randomly-generated practice problem, click the ‘New problem’ button above.

Think about your answer, and then press ‘Enter’ or ‘Check your answer’.
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