# Algebraic - Issue with simple equation problem

I have this equation: $x+7-(\frac{5x}8 + 10) = 3$

I've used step-by-step calculators online but I simply don't understand it. Here is how I've tried to solve the problem:

$$x+7-\left(\frac{5x}8+10\right) = x + 7 - \frac{5x}8 - 10 = 3$$

$$x + 7 - \frac{5x}8 - 10 + 10 = 3 + 10$$

$$x + 7 - 7 - \frac{5x}8 = 13 - 7$$

$$x - \frac{5x}8 = 6$$

$$x - 8\times\frac{5x}8 = 6\times8$$

$$x - 5x = 48$$

$$\frac{-4x}{-4} = \frac{48}4$$

$$x = -12$$

Now obviously, it's wrong. The right answer is $16$, but I don't know how to get to that answer. Therefore, I'm extremely thankful if someone truly can show what I need to do, and why I need to do it, because I'm completely lost right now. Thanks.

## 5 Answers

At the line :

$$x - 8\times \frac{5x}8 = 6\times 8$$ you should instead write $$8\times(x-\frac{5x}8) = 6 \times 8.$$

Indeed, you're multiplicate the entire left side and the entire right side of your equation.

Note that you can also calculate $x-\frac{5x}8 = \frac{8x}8 - \frac{5x}8 = \frac{3x}8$.

$x-8\cdot\frac{5x}{8}=6\cdot8$ is wrong, it should be $8x-8\cdot\frac{5x}{8}=6\cdot8$. Then you get $3x=48$, or $x=16$.

4th line from the end you forgot to multiply the $x$ by 8 as well.

You just need to rearrange the equation as follows:

$x+7-(\frac{5x}{8}+10) = 3$

$\frac{3x}{8} -3 = 3$

$\frac{3x}{8} = 6$

$3x = 48$

$x = 16$

If I've gone a bit too quickly please let me know and I'll add a few intermediate steps.

$x+7-(\frac{5x}{8}+10)=3$

$\Rightarrow x+7-(\frac{5x+80}{8})=3$

$\Rightarrow x+7+\frac{-5x-80}{8}=3$

$\Rightarrow \frac{8x+7*8-5x-80}{8}=3$

$\Rightarrow \frac{8x+7*8-5x-80}{8}=3$

$\Rightarrow 8x+56-5x-80=3*8$

$\Rightarrow 8x-5x=24+80-56$

$\Rightarrow 3x=48$

$\Rightarrow x=16$