To solve the equation and find the value of z, we'll first simplify the equation:
55 - (z - 45) = 62
Distribute the negative sign to the terms inside the brackets:
55 - z + 45 = 62
Combine like terms:
100 - z = 62
Let's isolate z by subtracting 100 from both sides:
- z = 62 - 100
Simplify:
- z = -38
To get z alone, we can multiply both sides of the equation by -1:
z = -(-38)
Simplify:
z = 38
So, the value of z is 38.
Let's check our answer by substituting z = 38 back into the original equation:
55 - (38 - 45) = 62
Simplify:
55 - (-7) = 62
Apply the double negative:
55 + 7 = 62
Simplify:
62 = 62
Since both sides of the equation are equal, our solution is correct.
