1. Equations Question

Hello All!

I could really use some guidance in how to solve these two equations. They are probably really simple but I am having trouble finding examples similar to these in my textbook. I don't need the answers just some tips on how to go about solving these. Just looking at them puzzles me. I don't know how to start them. The first thing that pops into my head is to get rid of the fractions with a Common Den. but I am unsure if that is correct. Any tips on how to solve would be very appreciated! Thankyou!

Rose

#1)

z
_ = 2z + 35
2

#2)

1 1 -2t
__ - __ = ____
t-2 2 4t-1

This last problem is supposed to be one over t-2 minus one half equals negative 2t over 4t-1 .... hope that helps to understand it

2. Originally Posted by Yup318
Hello All!

I could really use some guidance in how to solve these two equations. They are probably really simple but I am having trouble finding examples similar to these in my textbook. I don't need the answers just some tips on how to go about solving these. Just looking at them puzzles me. I don't know how to start them. The first thing that pops into my head is to get rid of the fractions with a Common Den. but I am unsure if that is correct. Any tips on how to solve would be very appreciated! Thankyou!

Rose

#1)

z
_ = 2z + 35
2

#2)

1 1 -2t
__ - __ = ____
t-2 2 4t-1

This last problem is supposed to be one over t-2 minus one half equals negative 2t over 4t-1 .... hope that helps to understand it
1. $\frac{z}{2} = 2z + 35$

$z = 4z + 70$

$-3z = 70$

$z = -\frac{70}{3}$.

2. $\frac{1}{t-2} - \frac{1}{2} = -\frac{2t}{4t - 1}$

$\frac{1}{t-2} + \frac{2t}{4t - 1} = \frac{1}{2}$

$\frac{4t - 1}{(t-2)(4t - 1)} + \frac{2t(t - 2)}{(t-2)(4t-1)} = \frac{1}{2}$

$2[4t - 1 + 2t(t-2)] = (t-2)(4t-1)$

$2(4t - 1 + 2t^2 - 4t) = 4t^2 - t - 8t + 2$

$4t^2 - 2 = 4t^2 - 9t + 2$

$9t = 4$

$t = \frac{4}{9}$.

3. thank you!!