Solve the compound inequality.
>−2x3−11
or
≥+3x36
Write the solution in interval notation.
If there is no solution, enter
∅
.
Bruh
To solve the compound inequality, we will solve each inequality separately and then combine the solutions.
For the first inequality:
-2x + 3 > -11
Adding 2x to both sides gives:
3 > -11 + 2x
Simplifying:
14 > 2x
Dividing both sides by 2 gives:
7 > x
For the second inequality:
3x + 3 ≥ 36
Subtracting 3 from both sides gives:
3x ≥ 33
Dividing both sides by 3 gives:
x ≥ 11
Combining the solutions, we have:
x ∈ [11, ∞) or x ∈ (-∞, 7]
Therefore, in interval notation, the solution is:
(-∞, 7] ∪ [11, ∞)
To solve the compound inequality, we will solve each inequality separately and then combine the solutions.
Let's start with the first inequality: -2x + 3 > -11
Subtract 3 from both sides:
-2x > -11 - 3
-2x > -14
Divide both sides by -2, remembering to reverse the inequality sign because we are dividing by a negative number:
x < (-14)/(-2)
x < 7
Now let's move on to the second inequality: 3x + 3 ≥ 36
Subtract 3 from both sides:
3x ≥ 36 - 3
3x ≥ 33
Divide both sides by 3:
x ≥ 33/3
x ≥ 11
Now, let's combine the solutions of both inequalities:
The first inequality tells us that x is less than 7, and the second inequality tells us that x is greater than or equal to 11. Since these two conditions cannot be simultaneously true, there is no overlap between the solutions. Therefore, there is no solution to the compound inequality.
In interval notation, we represent the solution set as ∅ since there are no values that satisfy both inequalities.