'OR" COMPOUND INEQALITY
1-X>_-3 OR 5X - 1 > 19
1-x >= -3
x <= 4
5x-1 >= 19
5x >= 20
x >= 4
Looks like all real numbers.
Thank You
To solve the compound inequality 1 - X ≥ -3 OR 5X - 1 > 19, we need to solve each inequality separately and then combine the solutions.
Let's start with the first inequality:
1 - X ≥ -3
To isolate X, we'll subtract 1 from both sides of the inequality:
1 - X - 1 ≥ -3 - 1
-X ≥ -4
Now, we'll multiply both sides by -1. Remember to reverse the inequality because we are multiplying by a negative number:
-X × (-1) ≤ -4 × (-1)
X ≤ 4
So, the solution to the first inequality is X ≤ 4.
Now, let's move on to the second inequality:
5X - 1 > 19
To isolate X, we'll add 1 to both sides:
5X - 1 + 1 > 19 + 1
5X > 20
Next, we'll divide both sides by 5:
5X/5 > 20/5
X > 4
So, the solution to the second inequality is X > 4.
Now, let's combine the solutions using the "OR" operator. Since X can either be less than or equal to 4 (X ≤ 4) or greater than 4 (X > 4), the solution set is the union of both:
X ≤ 4 OR X > 4
This means X can take any value less than or equal to 4, or any value greater than 4.