Linear equation help

Question

$$\frac{1-x}{4} + \frac{5x+1}{2} = 3 - \frac{2(x+1)}{8}$$

I got x=1 but the book says x=4/5 and I don't understand how to get to that, I tried working backwards too but I just can't figure it out. Any help would be appreciated, thanks.

Here's my work using 8 as the lcm $$ \begin{align} \frac 81(\frac {(1-x)}4) + \frac 81(\frac {(5x+1)}2) &= \frac 81(3) - \frac 81\frac {2(x+1)}8 \\ 2(1-x) + 4(5x+1) &= 24 - 2x + 2 \\ 2 - 2x + 20x + 4 &= 24 - 2x + 2 \\ 6 + 18x &= 26 -2x \\ 20x &= 20 \\ x &= 1 \\ \end{align} $$

Answer 1

You have a sign mistake here $$2(1-x) + 4(5x+1) = 24 - 2x \color{red}{+ 2}$$ It should be $$2(1-x) + 4(5x+1) = 24 - 2x \color{blue}{- 2}$$

Because $$-\frac {2(x+1)}8 =-\frac x4-\frac 14$$

Answer 2

Get everything over as a fraction with a denominator of $8$ and equate, so:

$$\frac{2(1-x)}{8}+\frac{4(5x+1)}{8}=\frac{24}{8}-\frac{2(x+1)}{8}$$

Thus we have: $$2-2x+20x+4=24-2x-2$$

See if you can go from there.

Answer 3

We have that

$$\frac{1-x}{4} + \frac{5x+1}{2} = 3 - \frac{2(x+1)}{8}\iff 2(1-x)+4(5x+1)=24-2(x+1)\\\iff2-2x+20x+4=24-2x-2\iff20x=16$$