Please help! They are asking for 2 solution sets and I don't know where to start. Thanks in advance!
Solve and write interval notation for the solution set.
3 – 8x < –5 or 3 – 8x > 19
Solve each part independently:
3 - 8x < -5
-8x < -8
x > 1
3 - 8x > 19
-8x > 16
x < -2
Therefore, the solution is [-infinity, -2] and [1, infinity]
Would this
[-infinity, -2] and [1, infinity]
be the same and equal
(-infinity sign,-2, U(1,infinity sign)
Yes. I should have used parentheses.
It's ok, I see how this is the answer now! Thanks again for your help!
To find the solution set for the given inequality, we need to solve each inequality separately and then combine the solution sets.
Let's start with the first inequality:
3 – 8x < –5
To solve this inequality, we'll isolate the variable x. Let's subtract 3 from both sides:
3 – 8x - 3 < –5 - 3
-8x < -8
Now, we'll divide both sides of the inequality by -8. Since we're dividing by a negative number, the inequality sign flips:
-8x / -8 > -8 / -8
x > 1
So, the solution set for the first inequality is x > 1.
Now let's move on to the second inequality:
3 – 8x > 19
To solve this inequality, we'll again isolate the variable x. Let's subtract 3 from both sides:
3 – 8x - 3 > 19 - 3
-8x > 16
Next, we'll divide both sides of the inequality by -8. Remember, when we divide by a negative number, the inequality sign again flips:
-8x / -8 < 16 / -8
x < -2
So, the solution set for the second inequality is x < -2.
Now, we need to combine the solution sets for both inequalities. Since the question asks for the union of the solution sets, we'll use the symbol ∪ (read as "union").
The solution set in interval notation is (-∞, -2) ∪ (1, ∞).