Final answer:
After rearranging and simplifying the equation 40x + 20 = 4(x - 7), we find the solution x = -4/3, which in interval notation is written as [-4/3, -4/3]. There is no inequality in the original question; it's a straightforward equation yielding a single-value solution.
Step-by-step explanation:
To solve the inequality 40x + 20 = 4(x - 7), first expand the right side of the equation by distributing the 4, which gives us 40x + 20 = 4x - 28. Next, subtract 4x from both sides to get 36x + 20 = -28. Then, subtract 20 from both sides to get 36x = -48. Dividing both sides of the equation by 36 gives us x = -43. Since this is not an inequality but an equation, we have a single-value solution which in interval notation is simply [-43, -43].
It appears that this problem is straightforward and does not generate an inequality solution, rather a single value for x. It was possibly intended to be an inequality and the student has written the problem incorrectly, but based on the information provided, this is the given solution.