Let's find the value for x in the next inequality:
[tex]-2x-6\text{ < 5x-3}[/tex]Add both sides 6:
[tex]-2x-6+6<5x-3+6[/tex][tex]-2x<5x+3[/tex]Now, subtract both sides by 5x
[tex]-2x-5x<5x-5x+3[/tex][tex]-7x<3[/tex]Multiply both sides by -1
When we multiply by a negative number, the inequality changes. In this case from "<" to ">".
Therefore:
[tex](-1)(-7x)<(-1)(3)[/tex][tex]7x<-3[/tex]Finally, divide both sides by 7
[tex]\frac{7x}{7}>\frac{-3}{7}[/tex][tex]x<\frac{-3}{7}[/tex]