Question

Is about inequalities, I know the rule of flipping the sign if you multiply or divide by a negative numbers but a few examples confuse me.

To make this inequality 5x+2y<14 into the slope-intercept form y=mx+b, please tell me if the sign has to be flipped.
I do it like this
5x+2y<14
y<-5/2x+14/2
y<-5/2x+7
I am not dividing by a negative number but 5 is negative, 2 is positive, should I flip the sign or not?

Answer 1

do not flip the sign

Explanation:

you only flip when you divide with negative number

however, for you to get the intercepts, you assumed

for y =0

5x +2(0)<14

5x<14

x<14/5<2.8

and also

x=0

5(0)+2y<14

2y<14

y<14/2

y<7

this assumption is because at interception, either x or y will be at origin