Checking solutions of two-variable linear inequalities example | Algebra I | Khan Academy | Summary and Q&A

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March 8, 2011
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Checking solutions of two-variable linear inequalities example | Algebra I | Khan Academy

TL;DR

Determine if given ordered pairs are solutions to the inequality 5x - 3y ≥ 25 by substituting the values of x and y and evaluating the inequality.

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Questions & Answers

Q: How do you determine if an ordered pair is a solution to an inequality?

To determine if an ordered pair (x, y) is a solution, substitute the values of x and y into the inequality and check if it is true. If the inequality is satisfied, the ordered pair is a solution; otherwise, it is not.

Q: What is the significance of the greater-than or equal-to symbol in the inequality?

The greater-than or equal-to symbol (≥) in the inequality indicates that values satisfying the equation, including the line itself, are part of the solution. It allows for inclusion of the boundary line in the solution area.

Q: What does it mean when an inequality swaps the inequality sign after dividing or multiplying by a negative number?

When an inequality is multiplied or divided by a negative number, the inequality sign swaps. For example, if you divide both sides by -3, the greater than or equal to (≥) sign becomes less than or equal to (≤). This is because negative multiplication or division alters the direction of inequality.

Q: How can graphing an inequality help visualize its solution?

Graphing an inequality provides a visual representation of the solution area. The line represents the equation itself, and the shaded area or region below the line represents the values that satisfy the inequality. The solution can be easily seen by analyzing the points within and outside the shaded region.

Summary & Key Takeaways

  • The content explains how to determine if ordered pairs are solutions to an inequality.

  • Two ordered pairs, (3, 5) and (1, -7), are tested in the inequality 5x - 3y ≥ 25.

  • Substituting the values of x and y in the inequality, (3, 5) does not satisfy it while (1, -7) does.

  • The inequality is graphed, showing the solution area and where the given ordered pairs lie.

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