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Graphing Linear Inequalities Practice Problems

Decide the line style, then the side to shade, and check with a test point. The later problems include a sign flip and vertical boundaries.

  1. 1.

    Is the boundary line of solid or dashed?

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    is strict, so points on the line aren’t solutions: dashed.

  2. 2.

    Is the boundary line of solid or dashed?

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    includes equality, so the line is solid.

  3. 3.

    For , do you shade above or below the line?

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    is isolated and greater than, so shade above.

  4. 4.

    For , do you shade above or below the line?

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    is isolated and less than or equal, so shade below.

  5. 5.

    Is a solution of ? Answer yes or no.

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    is true.

  6. 6.

    Is a solution of ? Answer yes or no.

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    , and is false.

  7. 7.

    Is a solution of ? Answer yes or no.

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    is true, so the origin’s side is shaded.

  8. 8.

    What is the -intercept of the boundary line of ?

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    Set : , so .

  9. 9.

    Rewrite as or . What is ?

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    Divide by and flip the sign: , so .

  10. 10.

    After rewriting with alone, do you shade above or below?

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    Dividing by flips the sign: , so shade below.

  11. 11.

    For , is the boundary line vertical or horizontal?

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    is a vertical line; shade to its right.

  12. 12.

    A graph has a dashed boundary with the region below it shaded. Which symbol completes ? Type <, >, <= or >=.

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    Dashed means strict, and below means less than: .
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Graphing Linear Inequalities Practice Problems

These problems follow the graphing linear inequalities lesson. Use a test point whenever isn’t on its own.

The four cases

InequalityLineShade
dashedabove
solidabove
dashedbelow
solidbelow

Common mistakes to watch for

  • Wrong line type. Use a dashed line for or , a solid line for or .
  • Shading the wrong side. Test a point such as : if it satisfies the inequality, shade its side.
  • Not flipping when dividing by a negative. Solving for and dividing by a negative reverses the inequality sign.
  • Using the origin when the line passes through it. Choose another test point, such as .

Frequently Asked Questions

How do I answer these?+

Type solid or dashed, above or below, yes or no, or a number, as each question asks.

When does the inequality sign flip?+

When you multiply or divide both sides by a negative number, for example when dividing by the coefficient of y if it is negative.

More practice problems

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