Enter your answer and show all the steps that you use to solve this problem in the space provided. Write an inequality for the graph. The answer is y=|5-x|+1

Answer 1

To write an inequality for the graph y = |5-x| + 1, we need to understand the properties of absolute value.

For any real number x, the absolute value of x (denoted as |x|) is defined as the distance of x from 0 on the number line. This means that if x is positive or negative, |x| will always be positive.

In this case, the expression |5-x| represents the distance of (5-x) from 0. The value of (5-x) can be positive or negative, but the absolute value will always be positive.

Adding 1 to the absolute value gives us |5-x| + 1, which shifts the graph of |5-x| one unit upward.

Therefore, the inequality for the given graph is y ≥ 1. This means that y is greater than or equal to 1.

Alternatively, if you want to write the inequality in terms of x, you can isolate x in the equation y = |5-x| + 1:

1. Subtract 1 from both sides: y - 1 = |5-x|
2. Remove the absolute value by considering both cases of (5-x):
a. If 5-x is positive or zero, then |5-x| = 5-x. So the equation becomes y - 1 = 5-x.
b. If 5-x is negative, then |5-x| = -(5-x) = x-5. So the equation becomes y - 1 = x-5.
3. Rearrange the equations to solve for x:
a. If 5-x is positive or zero: y - 1 = 5-x
--> x - y = -4
b. If 5-x is negative: y - 1 = x-5
--> -x - y = -4
4. The inequality for the graph is either x - y ≥ -4 or -x - y ≥ -4 (depending on the value of 5-x).

Thus, the inequality for the graph is x - y ≥ -4 or -x - y ≥ -4.