solve the compound inequality write the solution in interval notation 2u+4>-6 and 3u-6> -3
2u>-10
U>-5
and
3u>3
u>1
If you draw this on a number line, you would have an open circle or ( at -5 and your arrow will go to the right. You will have the same at 1 with your arrow going to the right.
Since it is "and" the answer is where they overlap.
the overlap begins at 1 and goes to infinity.
Interval notation: (1, infinity)
To solve the compound inequality 2u + 4 > -6 and 3u - 6 > -3, we'll solve each inequality separately and then combine the solutions.
First inequality:
2u + 4 > -6
Subtract 4 from both sides:
2u > -10
Divide both sides by 2:
u > -5
Second inequality:
3u - 6 > -3
Add 6 to both sides:
3u > 3
Divide both sides by 3:
u > 1
Now let's combine the solutions:
The solution to the compound inequality is u > 1.
In interval notation, this is written as (1, ∞), meaning u is greater than 1, but not including 1.
To solve the compound inequality, let's break it down into two separate inequalities and solve them individually.
First inequality:
2u + 4 > -6
Subtract 4 from both sides:
2u > -10
Divide both sides by 2 (since 2u means u multiplied by 2):
u > -5
Second inequality:
3u - 6 > -3
Add 6 to both sides:
3u > 3
Divide both sides by 3:
u > 1
Now, let's combine the two inequalities. Since both inequalities have a greater than sign, we are looking for the values of u that are greater than both -5 and 1.
So, the solution in interval notation would be (1, ∞), indicating that u is greater than 1 and is not restricted from extending towards positive infinity.