Algebraic Inequalities Practice Questions

Practice 2

1. Add 4 to each part of the inequality:

   0 < x – 4 ≤ 4

   4 < x ≤ 8

   Because x is greater than 4, 4 is not part of the solution set, and because x is less than or equal to 8, 8 is part of the solution set. Draw a hollow circle around 4 and a closed circle around 8. Shade the area between them:

   

2. Divide by –7 and change the inequality symbols from greater than to less than:

   49 > –7x > –21

   –7 < x < 3

   Because x is greater than –7, –7 is not part of the solution set, and because x is less 3, 3 is not part of the solution set. Draw a hollow circle around –7 and a hollow circle around 3. Shade the area between them:

   

3. Add 7 to each part of the inequality and divide by 3:

   –13 ≤ 3x – 7 < 20

   –6 ≤ 3x < 27

   –2 ≤ x < 9

   Because x is greater than or equal to –2, –2 is part of the solution set, and because x is less than 9, 9 is not part of the solution set. Draw a closed circle around –2 and a hollow circle around 9. Shade the area between them:

   

4. Subtract 1 from each part of the inequality and multiply by 5:

   

   

   0 ≥ x ≥ –10

   Because x is less than or equal to 0, 0 is part of the solution set, and because x is greater than or equal to –10, –10 is part of the solution set. Draw a closed circle around 0 and a closed circle around –10. Shade thearea between them:

   

5. Add 5 to each part of the inequality and multiply by –2. Change the inequality symbols from greater than and greater than or equal to to less than and less than or equal:

   

   

   –8 < x ≤ –4

   Because x is greater than –8, –8 is not part of the solution set, and because x is less than or equal to –4, –4 is part of the solution set. Draw a hollow circle around –8 and a closed circle around –4. Shade the area between them:

   

Practice 3