solve the compound inequality write the solution in interval notation
2u+4>-6 and 3u-6> -3 =
Solve each one individually:
2u >-2
u > -1
3u > 3
u >1
Draw a number line and put an open circle or a ( at -1 and 1
from -1 you will draw an arrow to the right on the number line
from 1 you will draw an arrow to the right on the number line.
AND means your answer is where the arrows overlap.
The overlap should start at 1 and to to infinity.
The final answer is x>1
To solve the compound inequality 2u + 4 > -6 and 3u - 6 > -3, we will solve each inequality separately and then combine the solutions.
1. Solve the first inequality, 2u + 4 > -6:
Subtract 4 from both sides:
2u + 4 - 4 > -6 - 4
2u > -10
Divide both sides by 2:
2u/2 > -10/2
u > -5
2. Solve the second inequality, 3u - 6 > -3:
Add 6 to both sides:
3u - 6 + 6 > -3 + 6
3u > 3
Divide both sides by 3:
3u/3 > 3/3
u > 1
Now, we will combine the solutions by looking for the overlapping region:
Since both inequalities are greater than, the overlapping area is where both solutions are true. In this case, both u > -5 and u > 1 will be true when u is greater than 1.
Therefore, the solution to the compound inequality is u > 1.
In interval notation, we represent the solution as (1, ∞), which means all the numbers greater than 1.