-2 |h-7|= -28
You have two cases:
h-7 >=0, where |h-7| = h-7
h-7 < 0, where |h-7| = -(h-7)
So,
case 1: h-7 >= 0 (h >= 7)
-2(h-7) = -28
h-7 = 14
h = 21
Since 21 >= 7, it's a solution
Case 2: h-7 < 0 (h < 7)
-2(-(h-7)) = -28
2h-14 = -28
2h = -14
h = -7
Since -7 < 7, it's a solution
So, h=-7,21
Another way to look at it is to say
-2|h-7| = -28
|h-7| = 14
That means that h has to be at a distance of 14 from 7, either above or below. So, h = -7 or 21
To solve the equation |-2|h-7|= -28, we need to isolate the absolute value expression and then consider two cases.
Case 1: (h-7) is positive or zero
Since the absolute value of any non-negative number is the number itself, we can rewrite the equation as -2(h-7) = -28.
Distributing -2 to both terms inside the parentheses, we get -2h + 14 = -28.
Now, isolate the variable by subtracting 14 from both sides: -2h = -42.
Dividing both sides of the equation by -2, we find that h = 21.
So, when (h-7) is positive or zero, the solution is h = 21.
Case 2: (h-7) is negative
When (h-7) is negative, the absolute value turns it into a positive value. Thus, we can rewrite the equation as -2(-h+7) = -28.
Simplifying the equation by distributing -2, we have 2h - 14 = -28.
Move -14 to the right side of the equation by adding 14 to both sides: 2h = -14.
Dividing both sides by 2, we find that h = -7.
So, when (h-7) is negative, the solution is h = -7.
In conclusion, the equation |-2|h-7|= -28 has two possible solutions: h = 21 and h = -7.