Question

how do I solve this? 10 - 5/x < -7

Answer 1

x/5 not 5/x sorry!!

Answer 2

Is that \[\frac{10-x}{5} < -7\]or\[10-\frac{x}{5}< -7\]

Answer 3

the second one.

Answer 4

okay. many people meaning the first one will write what you wrote, so I have to ask...

\[10-\frac{x}{5} = -7\]Would you know how to solve that?

Answer 5

no

Answer 6

Well, then you need to learn, or you're going to have a very unpleasant time in your math classes!

The general principle is that you can do anything you want (add, subtract, multiply, divide, etc.) as long as you do it to both sides of the equation.

For example, \[2+2=4\]We can add \(3\) to both sides:
\[2+2+3 = 4+3\]\[7=7\]Still balanced.


We could divide each side by 2:\[2+2=4\]\[\frac{2}{2}+\frac{2}{2} = \frac{4}{2}\]\[1+1=2\]\[2=2\]Still balanced.

We could multiply each side by -1:
\[(-1)*2 + (-1)*2 = -1*4\]\[-2-2 = -4\]\[-4=-4\]Still balanced.

Answer 7

So we need to pick a set of operations that will transform \[10-\frac{x}{5} < -7\]into something like \[x<3\]

I would suggest first multiplying by \(5\), which will get rid of that pesky fraction term.
\[5*10 - 5*\frac{x}{5} < 5*(-7)\]\[50 - x < -35\]That looks promising. Now if we can get rid of that \(50\) on the left side and change \(-x\) to \(x\), we'll be all set!

How can we get rid of that \(50\)? How about subtracting it (again, from both sides, to preserve the equation)?

\[50 - 50 - x < -35 - 50\]\[-x<-85\]

Now we just need to convert that \(-x\) to \(x\). Hopefully, you remember that \(-1*-1 = 1\), so we can multiply \(-1*-x = x\). Here's the tricky part: when you have an inequality, if you multiply or divide by a negative number, you have to remember to change the direction that the inequality sign points. If you have \(<\text{ or }\le\) it becomes \(\ge\text{ or }>\). If you have \(>\text{ or } \ge\) it becomes \(<\text{ or }\le\).

So, let's multiply by \(-1\) and change the direction of the inequality sign:
\[-1*-x < -1*-85\]\[x > 85\]
That's it!