2(0.5-3y) + y > (4y-0.2)8
I understand how to solve the problem, but my final answer was y < -17/155, which I have a strange feeling isn't right. Maybe I tripped up somewhere. Here's my work:
After distributing:
1-6+y>32y-1.6
+6 to each side
1 +y > 32y + 4.4
-1 to both sides
y > 32y + 3.4
-32y to both sides
-31y > 3.4
divide both sides by -31
And I got the answer y < -17/155
Do you know where I messed up?
Thanks so much!
You made a mistake in your first line, left side.
1 - 6y + y > 16y -1.6
Combine constants on one side and y-terms on the other.
2.6 > 21 y
y < 2.6/21 = 13/105
How did you get 16y instead of 32y? 8 times 4 is 32...
Thanks!
To solve the inequality correctly, let's go through the steps again and identify where you may have made a mistake.
Starting with the original inequality:
2(0.5 - 3y) + y > (4y - 0.2)8
First, let's distribute the multiplication:
1 - 6y + y > 32y - 1.6
Combining like terms:
1 - 5y > 32y - 1.6
Next, let's isolate the variable terms on one side and the constant terms on the other side. So, subtract 32y from both sides:
1 - 5y - 32y > -1.6
Simplifying:
-37y + 1 > -1.6
Subtract 1 from both sides:
-37y > -2.6
Now, it seems that you made an error after this step. When dividing both sides by -37, remember to reverse the inequality sign since you are dividing by a negative number:
y < -2.6 / -37
Simplifying further:
y < 0.07
So, the correct solution is y < 0.07, not y < -17/155.
It's essential to be careful with signs when dividing by a negative number, especially when dealing with inequalities.