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Equations and Inequalities

Equations and Inequalities

Solving Inequalities Exercises

Example 1

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

Example 2

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

Example 3

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

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. 

Example 5

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

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. 

Example 7

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

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.