Chapter 2.5, Problem 28E

To determine

To solve: The given inequality.

Answer to Problem 28E

Here, the given inequality $x-8\le 4or2x+3>9$ is the set of all real numbers.

Explanation of Solution

Given: $x-8\le 4or2x+3>9$

Calculation:

Equation 1:

  $x-8\le 4$

Add both sides by $8$

  $x-8+8\le 4+8$

Reverse inequality symbol

  $x\le 12$

Equation 2:

  $2x+3>9$

Subtract both sides by $3$

  $2x+3-3>9-3$

Divide both sides by $2$

  $\frac{2x}{2}>\frac{6}{2}$

Simplify

  $x>3$

Since the inequality is $y\le 12orx>3$ and uses the word “or”, its solution set should be the union of the two graphs.

Therefore, its graph should have an open point at $3$ and a shaded line going to the right of $3$ and a closed point at $12$ , and a shaded line going to the left or the set all real numbers, as in: as in:

  

Conclusion:

Therefore, the given inequality $x-8\le 4or2x+3>9$ is the set of all real numbers.