Solve 3(3-8x)+5<2(9+6x)

Use set builder notion to describe the solution?

I got x=9/31 is this correct???

3(3-8x)+5<2(9+6x)

Expand both sides:
9-24x+5 < 18+12x
Add 24x to each side:
14 < 36x+18
Subtract 18 from each side:
-4 < 36x
Change sides:
36x>-4
x>1/9

Solution set:
{x : x>1/9}

To solve the inequality 3(3-8x) + 5 < 2(9+6x), we will follow these steps:

Step 1: Distribute the terms inside the parentheses:
6 - 24x + 5 < 18 + 12x

Step 2: Combine like terms on both sides:
11 - 24x < 18 + 12x

Step 3: Move variable terms to one side by adding 24x to both sides:
11 < 18 + 36x

Step 4: Move constant terms to the other side by subtracting 18 from both sides:
11 - 18 < 36x
-7 < 36x

Step 5: Divide both sides of the inequality by 36 (since it is a positive number):
-7/36 < x

Now, let's express the solution using set builder notation. The solution is all the values that x can hold to satisfy the inequality. In this case, x must be greater than -7/36.

Therefore, the set builder notation for the solution would be:
{x | x > -7/36}

Regarding your answer of x = 9/31, it is not correct. The correct solution is x > -7/36, meaning any value of x that is greater than -7/36 will satisfy the inequality.