Let's look at the two given inequalities. Notice that the inequality x -5 ≤ 6-5 can be obtained from x ≤ 6 by performing subtraction on both sides of the inequality.
Subtracting the same number from each side of an inequality produces an equivalent inequality.
Therefore, subtracting 5 from each side of x ≤ 6 produces an equivalent inequality in the form of x - 5 ≤ 6 - 5. Let's visualize this property.
An inequality describes an order of two quantities on a number line. As we can see, subtracting the same number from both sides of the inequality does not change the distance between the quantities! This means that the distance between x-5 and 6-5 is the same as it was between x and 6. Therefore, if x is less than or equal to 6, then x-5 is less than or equal to 6-5.
