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Question 215442: Hello! I am not very good in math at all and would first like to thank you for taking out the time to help me! :)
I would like to know the solution to this problem: 6z+5=6(z+4)-19
Found 2 solutions by borja710, jsmallt9:
Answer by borja710(1)   (Show Source):
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! 6z+5=6(z+4)-19
There are three steps, in general, to solving equations like this:- Simplify each side of the equation.
- Get the variable on just one side of the equation.
- Isolate (i.e. "solve for") the variable
Step 1 (Simplify):
6z + 5 = 6(z+4) - 19
We can use the Distributive Property to multiply on the right side:
6z + 5 = 6z + 24 - 19
Now we can add the like terms:
6z + 5 = 6z + 5
At this point we might realize what is happening. But in case you don't see it, we'll continue.
Step 2 (Variable on one side): If the variable is on both sides, like in this equation, then this step is an addition or subtraction step.
So we want to eliminate the 6z on the right (or left). We can either add -6z to both sides or subtract 6z from both sides. When we do this the 6z cancels out, not only on the right side but also on the left! This leaves:
5 = 5
Most of the time we still have a variable at this point and we can proceed to step 3 and get a solution. And this solution is the single number which makes the original equation true.
The fact that no variable remains in the equation means one of two things:- All numbers are solutions to the equation.
- No numbers are solutions
There are a couple of ways to tell which is the case, all numbers or no numbers:- Pick a number, any number. Substitute that number into the original equation and see if it works. If it does then ALL numbers are solutions. If it does not work then NO numbers are solutions.
- Look at the variable-less equation. If it is a true statement, then ALL numbers are solutions. If it is a false statement (like 5 = -2), then NO numbers are solutions.
Either of these methods work. Usually the second one is easier.
Our variable-less equation, 5 = 5, is a true statement. So ALL numbers are solutions to the original equation.
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