Question

Solve each equation and check the result. If no solution so indicate.

Picture attached.

Answer 1

I know the answer is 2, 4. I've gotten the answer from a few different places and it's always the same, but when i try to do it myself it's impossible. I think i've just worked it too many times that it is almost like looking at a foreign language now. If someone could walk through the steps with me that would be amazing.

Answer 2

start with
\[a+\frac{3}{4}=\frac{3a-50}{4a-24}\] then add on the left
you get
\[\frac{4a+3}{4}=\frac{3a-50}{4a-24}\]"cross multiply" to get
\[(4a+3)(4a-24)=4(3a-50)\]cancel a 4 left and right to make it easier
\[(4a+3)(a-6)=3a-50\] and finally we can start to solve a quadratic equation

Answer 3

before solving we have to multiply out on the left
\[4a^2-21a-18=3a-50\] now set it equal to zero and solve
\[4a^2-24a+32=0\]

Answer 4

i would divide by 4 again to get
\[a^2-6a+8=0\] and this one factors as \((x-2)(x-4)=0\)
now you are done in one step

Answer 5

the only step i skipped was multiplying out
\[(4a+3)(a-6)\] all other steps are there

Answer 6

Thank you so much! You're a brain saver!

Answer 7

yw
hope all steps are clear