What would be the first step in |4x+3|=5x+7 ?

That's pretty simple, rosala....think of it like this....we're just taking something out of the absolute value "as is"  and solving one equation. And then, we're making it "negative" and solving a second equation. If you can solve the first equation, the second one isn't any tougher....!!!!

The first step is to create two equations:

1) 4x + 3 = 5x + 7

2) -(4x + 3) = 5x + 7 --> -4x - 3 = 5x + 7.

Aziz how did that minus sign come in front of four??in the second step?

Note, rosala, that if we have  lNl = 3

Then N might be +3  or -3

So...if we have

[4x + 3l = 5x + 7

Then we might have a "positive" (4x +3)  or a "negative" (4x + 3)

Does that make sense??

Here is the graph, https://www.desmos.com/calculator/j9gxp4g9wc 

Imagine if you continued to extend the lines. We would have two lines. One would have a positive slope and the other, a negative slope. The y-intercepts would be 3 and -3, and the slopes 4 and -4.

y = 4x +3 

y = -4x - 3

Can it be more simpler?

So its just this!Thats so simple!thanks for that CPhill!And u too Aziz!

A point for both!

Great questions Rosala.

When I see people questioning answers like you often do I know that learning is taking place. And that, really pleases me.