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# Equations and Inequalities

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# 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 *x* - 3 ≤ 2*x* and represent its solutions using a number line.

### Example 4

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

### Example 5

Solve the inequality -12*x* < 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 -7*y* + 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)] - 2*z*^{2}. Write the solution as an inequality, and show the solution on a number line.