Final answer:
The inequality 7x - 5 ≤ 13 + x simplifies to x ≤ 3 after subtracting x and adding 5 to both sides, and then dividing by 6. The solution represents all the values of x that are 3 or less.
Step-by-step explanation:
To solve the inequality 7x - 5 ≤ 13 + x, we need to first isolate the variable x on one side. To do this, we subtract x from both sides to get 6x - 5 ≤ 13. Next, we add 5 to both sides to get 6x ≤ 18. Finally, we divide both sides by 6 to find the solution to the inequality, which is x ≤ 3.
The answer means that the value of x must be less than or equal to 3 to satisfy the inequality. It's important to to see if it is reasonable, just as we eliminate terms wherever possible to simplify the algebra. This solution gives us a range of possible values for x that can be represented on a number line or a graph.