y>|5-x|+1
The given expression is |5-x| + 1.
To simplify this expression, we need to consider two cases:
Case 1: (5 - x) ≥ 0
If 5 - x is greater than or equal to zero, we can remove the absolute value symbols without changing the value. Therefore, |5 - x| becomes (5 - x).
The expression now becomes: (5 - x) + 1.
Simplifying further, we have: 6 - x.
Case 2: (5 - x) < 0
If 5 - x is less than zero, we need to negate the value inside the absolute value symbols. Therefore, |5 - x| becomes -(5 - x), which simplifies to (x - 5).
The expression now becomes: (x - 5) + 1.
Simplifying further, we have: x - 4.
Therefore, the simplified expression is:
if (5 - x) ≥ 0, then 6 - x.
if (5 - x) < 0, then x - 4.
To simplify the expression y = |5 - x| + 1, we can break it down into cases based on the value of (5 - x).
Case 1: (5 - x) ≥ 0
In this case, the absolute value is not necessary.
So, y = (5 - x) + 1
Simplifying further, y = 6 - x
Case 2: (5 - x) < 0
In this case, the absolute value becomes negative.
So, y = -(5 - x) + 1
Simplifying further, y = -5 + x + 1
y = x - 4
Thus, the simplified expression for y = |5 - x| + 1 is:
y = 6 - x if (5 - x) ≥ 0
y = x - 4 if (5 - x) < 0
The expression y = |5 - x| + 1 represents a mathematical function where the value of y depends on the value of x. To evaluate this expression, you need to understand how to handle absolute values and perform basic arithmetic operations.
Here's a step-by-step explanation on how to find the value of y for a given x:
1. Start with the expression |5 - x|. The absolute value symbol denotes the distance of the number inside it from zero on a number line. In this case, it represents the distance between 5 and x.
2. Determine the value inside the absolute value brackets, which is (5 - x). Here, you subtract x from 5.
3. Evaluate the absolute value by making the result positive. If (5 - x) is positive, the absolute value is equal to (5 - x). If (5 - x) is negative, the absolute value is equal to -(5 - x), which becomes (-5 + x).
4. Add 1 to the absolute value result. This is done by performing basic addition, using the evaluated value from step 3.
Finally, you have evaluated the expression and found the value of y.