Final answer:
The solution to the inequality (2x + 4 ≤ 16) or (4x + 11 > 51/4) is found by solving each inequality separately. The first part gives us x ≤ 6, and the second part gives us x > 10. The final answer is the union of both solutions, which is ((- ∞, 6] ∪ (10, ∞)).
Step-by-step explanation:
The student is asking to solve the inequality consisting of two parts, which are connected by the 'or' operator. We will solve each part separately and then consider the union of both solutions.
First inequality: (2x + 4 ≤ 16)
Subtract 4 from both sides: 2x ≤ 12.
Divide by 2: x ≤ 6.
So the solution to the first inequality is x ≤ 6, which in interval notation is (- ∞, 6].
Second inequality: (4x + 11 > 51/4)
Multiply 51/4 by 4 to convert to an integer: 51.
Subtract 11 from both sides: 4x > 40.
Divide by 4: x > 10.
So the solution to the second inequality is x > 10, which in interval notation is (10, ∞).
Combining both solutions with the 'or' operator means we take the union of both solution sets, therefore, the final answer is ((- ∞, 6] ∪ (10, ∞)).