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1+2z-5z-\left(-3\right)=4
To find the opposite of 5z-3, find the opposite of each term.
1+2z-5z+3=4
The opposite of -3 is 3.
1-3z+3=4
Combine 2z and -5z to get -3z.
4-3z=4
Add 1 and 3 to get 4.
-3z=4-4
Subtract 4 from both sides.
-3z=0
Subtract 4 from 4 to get 0.
z=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -3 is not equal to 0, z must be equal to 0.