Answer
- The solution of this compound inequality is x < 3 OR x ≥ 4
- The graph of this solution is attached below
- The interval notation is (-∞, 3) OR [4, ∞)
Explanation
The compound inequality to be solved is
6x - 3 < x + 12 OR 5x - 6 ≥ 3x + 2
To solve this, we solve each of the pair one at a time for the two-part solution
6x - 3 < x + 12
6x - x < 12 + 3
5x < 15
Divide both sides by 5
(5x/5) < (15/5)
x < 3
OR
5x - 6 ≥ 3x + 2
5x - 3x ≥ 6 + 2
2x ≥ 8
Divide both sides by 2
(2x/2) ≥ (8/2)
x ≥ 4
So, the solution is
x < 3 OR x ≥ 4
So, this solution says that x is less than 3, but greater than or equal to 4.
For the graph, Note that
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
This solution tells us that the wanted parts are numbers less than 3 and numbers greater than 4.
Also, in writing inequalities as interval, the signs (< or >) indicate an open interval and is written with the bracket () while the signs [≤ or ≥] denote a closed interval which is denoted by the brackets [].
x < 3, that is, x ranges from negative infinity to just before 3.
x < 3 is (-∞, 3)
x ≥ 4, that is, x ranges from 4 to infinity
x ≥ 4 is [4, ∞)
Hope this Helps!!!
