Linear Inequalities; Absolute Value!

Hellllo again,
As always, I hope everyone had a wonderful week/weekend!
This past week went by wayyy too fast..
Back to school tomorrow, see you all then!

Linear Inequalities: absolute value of 3x-1 <4 2x+3y>6
Polynomial Inequalities: x^3-x>0 y<3x^2-4x+1

1. You can add the same number to (or subtract the same number from) both sides of an inequality.
2. You can multiply (or divide) both sides of an inequality by the same positive number.
3. You can multiply (or divide) both sides of an inequality by the same negative number if you reverse the inequality sign.

**You flip the sign of the inequality when you multiply or divide by a negative number.

Example 1:
Solve the equation or inequality. If there is no solution, say so.
8x+6>30
subtract 6 from both sides
8x>24
divide both sides by 8
x>3

Example 2:
Solve the equation or inequality. If there is no solution, say so.
8-11x/4<13
8/4 simplifies to 2
2-11/4x<13
subtract 2 from both sides
-11/4x<11
multiply both sides by 4 to cancel the 4 in the fraction out
-11x<44
divide both sides by -11
since you divide by a negative, you flip the sign
x>-4