Asked by IDEK

Sam solved the following problem:

-4x + 5 > 29
-4x + 5 - 5> 29 - 5
-4x > -24/-4
x > 6

What was his TWO mistakes?
Sorry i am bad at this so i need help.
Answered by oobleck
after the 2nd line, the status stands at
-4x > 24
Now you can do
-4x/-4 > 24/-4
but that's wrong, since multiplying or dividing by a negative value changes the direction of the inequality. It would then be
-4x/-4 < 24/-4
x < -6

Or, you could just divide by 4, giving
-4x/4 > 24/4
-x > 6
x < -6

This changing direction is just a shorthand way of moving things to the other side of the inequality.
-4x > 24
add 4x to both sides: 0 > 24 + 4x
subtract 24 from both sides: -24 > 4x
That is just the same as 4x < -24
Now divide by 4 to get x < -6
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