Solve the equation for z?

Question

(z)/ (z+3) = (3z)/ (5z-1)

Answer 1

z/(z+3) = 3z/(5z-1)

Cross-Multiply in order to solve this. Cross-Multiplication states that, for variables a, b, c, and d:

if a/b = c/d, then ad = cb.

Plug in your values for this in order to solve for z:

3z(z+3) = z(5z-1)

Now use the distributive property:

3z² + 9z = 5z² - z

Subtract 3z² from both sides and combine like terms:

9z = 2z² - z

Next, subtract 9z from both sides and combine like terms:

0 = 2z² - 10z

Factor out 2z from the right side of this equation:

0 = 2z(z - 5)

Using this equation, a product of two numbers is equal to zero when one of the numbers is zero. So, in order for 2z or z - 5 to be zero, z must equal:

0 = 2z
0 = z

0 = z - 5
5 = z

Therefore:

z = 5 or 0

Hope this helps!

Answer 2

first we must do some rearranging and then it gets easier :)

(z)/ (z+3) = (3z)/ (5z-1)

if we multiply both sides by (z+3) and (5z-1) we get

(z)(5z-1) = 3z(z+3)

multiplying through

5z^2 - z = 3z^2 + 9z

rearranging

2z^2 - 10z = 0

so, we are now left with z^2 - 5z = 0 (we can get rid of the zero because we can divide both sides by 2, and 0/2 = 0)

Factorizing this gives us z(z-5) = 0 So, for this equation to ever be equal to zero, z = 0, or z = 5.

Answer 3

z (5z -1) = 3z (z + 3)
5z² - z = 3 z² + 9z
2z² - 10 z = 0
(2z) (z - 5) = 0
z = 0 , z = 5

Answer 4

first, cross multiply to get:

(5z-1)(z) =(3z)(z+3)

now, distribute each side:

5z^2 - z = 3z^2 + 9z

now, move all the terms to one side, setting the equation to zero:

2z^2 - 10z = 0

now, you can factor out a 2z to get:

2z (z -5) = 0

2z = 0
z-5 = 0

so z = 0 or z= 5

hope this helps!!

Answer 5

(z)/ (z+3) = (3z)/ (5z-1)
1. cross multiply: (z)(5z-1) = (3z)(z+3)
2. distribute: 5z^2 - z = 3z^2 + 9z
3. add like terms: 2z^2 - 10z = 0
4. factor 2z(z-5) = 0
5 solve: z = 0, 5.

Answer 6

z/(z+3)=(3z)/(5z-1)
cross multiply
z(5z-1)=3z(z+3)
5z^2-z=3z^2+9z
5z^2-z-3z^2-9z=0
2z^2-10z=0
2z(z-5)=0
z=0, z=5