Can someone please help me with this?
Use the set-builder notation to describe the solution.
3(3-8x)+5x<2(9+6x)
{x„ x ?,?}
Thank you
To describe the solution to the inequality using set-builder notation, we need to find the values of x that satisfy the inequality.
Let's start by simplifying the equation:
3(3 - 8x) + 5x < 2(9 + 6x)
First, distribute the multiplication:
9 - 24x + 5x < 18 + 12x
Combine like terms:
-19x + 9 < 18 + 12x
Next, isolate the variable terms on one side of the inequality:
-19x - 12x < 18 - 9
-31x < 9
Now, divide both sides of the inequality by -31. Remember that when we divide or multiply an inequality by a negative number, we need to flip the direction of the inequality sign:
x > 9 / -31 (Remember to flip the inequality sign)
Simplifying the division:
x > -0.290322581 (rounded to a reasonable decimal place)
So, the solution to the inequality is x > -0.290322581.
In set-builder notation, we designate the solution as:
{x | x > -0.290322581}
This means that x belongs to the set of real numbers, and x is greater than -0.290322581.