SOLVING INEQUALITIES

Example 1

Solve the inequality z + 5 ≥ 3 and represent its solutions using a number line

Answer

z ≥ -2

Example 2

Solve the inequality 4(x – 1) < 3(x + 1) and represent its solutions using a number line

Answer

x < 7

Example 3

Solve the inequality 2x + 3 ≤ x and represent its solutions using a number line

Answer

x ≤ -3

Example 4

Solve the inequality 5(x + 2) – 3x ≤ 4 + 2x + 3(x – 1). Write the solution as an inequality, and show the solution on a number line

Answer

3 ≤ x

Example 5

Solve the inequality -12x < 144. Write the solution as an inequality, and show the solution on a number line

Answer

x > -12

Example 6

Solve the inequality 5[x + 3(1 – x) + 2] ≥ 7. Write the solution as an inequality, and show the solution on a number line

Answer

 

Example 7

Solve the inequality 7y + 2 ≤ 65. Write the solution as an inequality, and show the solution on a number line

Answer

9 ≤ y

Example 8

Solve the inequality z + z[3 – 2(1 + z)] < 5[1 + 2(z – 3)] – 2z². Write the solution as an inequality, and show the solution on a number line

Answer

²⁵/₈ < z

Reference:

http://www.shmoop.com/equations-inequalities/solving-inequalities-exercises.html