Can someone please help me with this?
Use the set-builder notation to describe the solution.
3(3-8x)+5x<2(9+6x)
solve for x first
I got x<9/31 but check my work
then
{x│ x < 9/31 x is an element of ... } (you did not specify a domain, so probably R)
To solve the inequality 3(3-8x) + 5x < 2(9+6x), we can follow these steps:
1. Distribute the multiplication: 9 - 24x + 5x < 18 + 12x.
2. Combine like terms: 14 - 19x < 18 + 12x.
3. Move all the x terms to one side and all the constant terms to the other side: 14 - 18 < 19x + 12x.
This simplifies to: -4 < 31x.
4. Divide both sides of the inequality by 31 to solve for x: -4/31 < x.
Therefore, the solution to the inequality is x > -4/31.
Using set-builder notation, we can describe this solution as:
{x | x > -4/31}, where "x" represents the set of numbers greater than -4/31.