Solve the compound inequality.
>−2x3−11
or
≥+3x36
Write the solution in interval notation.
If there is no solution, enter
∅
.
<mumble>
x + 2 < -1 or -x < 9
To solve the compound inequality, we need to solve each inequality separately and then combine the solutions.
First, let's solve the inequality: -2x < 3 - 11
Adding 11 to both sides: -2x + 11 < 3
Subtracting 3 from both sides: -2x + 11 - 3 < 0
Combining like terms: -2x + 8 < 0
Now divide both sides by -2, remembering to reverse the inequality sign since we are dividing by a negative number: (-2x + 8)/-2 > 0/-2
Simplifying: x - 4 > 0
Next, let's solve the inequality: 3x ≥ 3(6)
Simplifying: 3x ≥ 18
Now divide both sides by 3: 3x/3 ≥ 18/3
Simplifying: x ≥ 6
Now we have the two inequalities solved separately:
x - 4 > 0 (Equation 1)
x ≥ 6 (Equation 2)
To obtain the compound solution, we need to find the intersection of the two solution sets.
From Equation 1, x must be greater than 4.
From Equation 2, x must be greater than or equal to 6.
To combine these solutions, we take the intersection, which means we take the values that satisfy both conditions.
The only values that satisfy both conditions are x > 6 because it also satisfies x > 4.
Therefore, the solution in interval notation is (6, ∞) since x must be greater than 6.
Note: If there were no values that satisfy both conditions, we would write the solution as ∅.