Just so you guys know, I'm not trying to get the answers to all of my assignment. These problems I'm posting are the ones that I'm stuck on.
6(4-3x)+4x<3(9+2x)
Use set-builder notation to describe solution.
{x/x_ _}
I'm not trying to just get answers. I'm trying to better understand the areas where I am not understanding things. As you all help me and put everything out in details, I'm writing down everything to better understand and reference back to if I get stuck again.
6(4-3x)+4x<3(9+2x)
24-18x+4x<27+6x
24<27+28x
-3<28x
(-3/28)<x
check my work
K, thanks and your last problem you helped me with was right.
Nice to hear that
I have a few problems that are on here that I was redirected to a website that I went to but still can't understand the problem. If you could try to help me with maybe some of those too, I'd greatly appreciate it. I only have a couple more problems I need help with besides the ones already on here. Thanks again hun.
fish
To solve the inequality 6(4-3x) + 4x < 3(9+2x), we'll follow these steps:
Step 1: Distribute the terms on both sides of the inequality:
24 - 18x + 4x < 27 + 6x
Step 2: Combine like terms:
24 - 14x < 27 + 6x
Step 3: Move all the x terms to one side and the constant terms to the other side of the inequality:
-14x - 6x < 27 - 24
Simplifying further:
-20x < 3
Step 4: Divide both sides of the inequality by the coefficient of x (-20 in this case), remembering that dividing by a negative number reverses the inequality sign:
x > 3 / -20
x > -0.15
So, the solution to the inequality is x > -0.15.
Now, let's express this solution using set-builder notation. Set-builder notation consists of two parts: the variable being restricted (x in this case) and the condition that must be satisfied.
In this case, the condition is that x must be greater than -0.15. So, we can express the solution in set-builder notation as:
{x | x > -0.15}
In this notation, the vertical bar "|" is read as "such that" and the inequality condition follows after it.