Final answer:
To solve the compound inequalities 3x-8 ≤ 23 OR -4x + 26 ≥ 6, we solve each inequality separately and find that the resulting solutions are x ≤ 31/3 and x ≤ 5. Since x ≤ 5 is the smaller upper limit, the final solution is x ≤ 5.
Step-by-step explanation:
To solve for x, we need to solve each inequality separately:
- 3x - 8 ≤ 23:
Add 8 to both sides:
3x ≤ 31
Then, divide both sides by 3:
x ≤ 31/3
- -4x + 26 ≥ 6:
Subtract 26 from both sides:
-4x ≥ -20
Then, divide both sides by -4 (remember to flip the inequality when dividing by a negative number):
x ≤ 5
The solution to the system of inequalities is the set of values that satisfy either of the inequalities. So, the values for x that satisfy at least one of the inequalities are all the values from -∞ up to ≤ 31/3 and from -∞ up to ≤ 5.
Since the second inequality gives a smaller upper limit on x, the solution for x from both inequalities considered together is:
x ≤ 5