For this case we have the following inequality:
[tex]-3 + 5x <7x-5[/tex]
Subtracting 7x from both sides of the inequality we have:
[tex]-3 + 5x-7x <-5[/tex]
Different signs are subtracted and the major sign is placed.
[tex]-3-2x <-5[/tex]
We add 3 to both sides of the inequality:
[tex]-2x <-5 + 3\\-2x <-2[/tex]
We divide between 2 on both sides of the inequality:
[tex]-x <\frac {-2} {2}\\-x <-1[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x> 1[/tex]
The solution is given by all the values of "x" greater than 1.
Answer:
[tex]x> 1[/tex]
