Solve the inequality. -x+37. I isolate the x, subtract -3 from both sides that gives me -x4 but the correct answer is x

Question

Solve the inequality. -x+3>7.  I isolate the x, subtract -3 from both sides that gives me -x>4 but the correct answer is x<-4 why did the sign flip since I didnt multiply or divide? what am I missing?

anonymous · Answer

$$3 > 7 + x$$

anonymous · Answer

$$-4 > x$$

anonymous · Answer

which could be written:
$$x < -4$$

anonymous · Answer

how did -x become just x?

anonymous · Answer

you add x to both sides of the inequality

anonymous · Answer

I was subtracting 3 from both sides

anonymous · Answer

$$-2 + 6 = 4$$ is the same as $$6 = 4 + 2$$

anonymous · Answer

I thought I missed a step

anonymous · Answer

You were doing it fine, but you want to get x by itself

anonymous · Answer

So, if we did it your way, then we would multiply each side by -1

anonymous · Answer

and that should give us the same result

anonymous · Answer

I think...

anonymous · Answer

exactly when you multiply you have to flip the sign.  I got it! Thank you