# Solving 3z/2=z/6+4: Is it Right?

• thomas576
In summary, the conversation discussed the first step in solving the equation 3z/2=z/6+4, which is to simplify by multiplying both sides by the common denominator. It also explained how to isolate the variable z by getting rid of attached numbers or terms, and emphasized that dividing both sides by z is not a viable method. To check the solution for z, one can substitute it back into the original equation. Other methods for solving this equation include using the distributive property and cross-multiplying, but the most efficient approach is to isolate the variable and solve for it.
thomas576
3z/2=z/6+4

so

i x multiply and get
18z=2z+8
16z=8

z=1/2

this look right?

thanks

Unfortunately no; you forgot to multiply your constant with 6 as well
(with the "constant", I mean the lone "4" in your original equation)

hmm

ok you lost me /shrug

3z/2=z/6+4
1. Multiply both sides of the equation with 6:
6*(3z/2)=6*(z/6+4)
OR:
18z/2=6z/6+6*4
Or:
9z=z+24
That is:
8z=24
Whereby:
z=3

Note:
I didn't bother with your cross-multiplication; that was an unnecessary operation.

## 1. What is the first step in solving the equation 3z/2=z/6+4?

The first step is to simplify the equation by multiplying both sides by the common denominator, which in this case is 6. This will eliminate the fractions and make the equation easier to solve.

## 2. How do I isolate the variable z in this equation?

To isolate the variable z, you need to get rid of any numbers or terms that are attached to it. In this equation, we can subtract z/6 from both sides to eliminate it from the right side. This will leave us with 3z/2-z/6=4.

## 3. Can I solve this equation by dividing both sides by z?

No, you cannot divide both sides by z in this equation. Doing so would result in 3/2=1/6+4/z, which does not simplify the equation. Instead, you should follow the steps of isolating the variable z and then solving for it.

## 4. How do I check if my solution for z is correct?

To check if your solution for z is correct, you can substitute it back into the original equation. If the equation is true, then your solution is correct. For example, if your solution is z=12, you can plug it back into the equation as 3(12)/2=12/6+4, which simplifies to 18=6+4, making the equation true.

## 5. Are there any other methods for solving this equation?

Yes, there are other methods for solving this equation, such as using the distributive property or cross-multiplying. However, the most efficient and straightforward method is to follow the steps of isolating the variable and then solving for it.

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