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Mathematics LibreTexts

2.1E: Exercises - Solving Linear Inequalities in One Variable

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Exercise 2.1E.1

Determine whether or not the given value is a solution.

  1. 5x1<2;x=1
  2. 3x+1>10;x=1
  3. 2x3<5;x=1
  4. 5x7<0;x=2
  5. 9y45;y=1
  6. 6y+13;y=1
Answer

1. Yes

3. No

5. Yes

Exercise 2.1E.2

Graph all solutions on a number line and provide the corresponding interval notation.

  1. 3x+5>4
  2. 2x+1>1
  3. 6a6
  4. 2a+5>5
  5. 5x+637
  6. 4x+11612
  7. 2(3x+14)<2
  8. 5(2y+9)>15
  9. 5x2(x3)<3(2x1)
  10. 3(2x1)10>4(3x2)5x
Answer

1. (3,);

a2d07ff66453c86a51eb9ee5ca94a731.pngFigure 1.8.13

3. [0,);

b071e41cd81d51aa4ebb4a13391c3cd2.png
Figure 1.8.14

5. (,3];

91d267fa92ccb40b4595195880f91df6.png
Figure 1.8.15

7. (,5);

2a7c54ebfc233db09481bb0a0bf08196.png
Figure 1.8.16

9. (3,);

46ffae560a1c8ea849b82a0d2ad14469.png
Figure 1.8.17

Footnotes

138Linear expressions related with the symbols ,<,, and >.

139A real number that produces a true statement when its value is substituted for the variable.

140Properties used to obtain equivalent inequalities and used as a means to solve them.

141Inequalities that share the same solution set.

142Two or more inequalities in one statement joined by the word “and” or by the word “or.”


2.1E: Exercises - Solving Linear Inequalities in One Variable is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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