8-|1-y|=7
8-1-y = 7 *absolute value sign removed
7-y = 7
-y=7-7
y=0
so there,, =)
The absolute value of a number is its'
distance from zero on the number line.
Therefore, the absolute value of 7 and
-7 is = 7. Your calculation is correct,
but 2 solutions are required to finish
the problem:
8 - [1 - y] = 7.
- [1 - y] = 7 - 8 = -1
[1 - y] = 1,
-(1 - y) = 1
-1 + y = 1
y = 2
Solution Set: y = 0 , y = 2.
To solve the equation 8-|1-y|=7, we need to isolate the absolute value expression and solve for y.
Let's break down the steps:
Step 1: Remove the absolute value by setting up two cases:
Case 1: 1-y is positive:
In this case, the absolute value can be removed, so 8-(1-y) = 7
Case 2: 1-y is negative:
In this case, the absolute value becomes -1-y. So, 8-(-1-y) = 7
Step 2: Solve for y in both cases:
Case 1: 8-(1-y) = 7
Simplify the left side:
8 - 1 + y = 7
7 + y = 7
Subtract 7 from both sides:
y = 0
Case 2: 8-(-1-y) = 7
Simplify the left side:
8 + 1 + y = 7
9 + y = 7
Subtract 9 from both sides:
y = -2
So, the solutions to the equation 8-|1-y|=7 are y = 0 and y = -2.