Answer
Step-by-step explanation
We are told to solve the compound inequality
5x + 8 > 23
OR
-4x + 6 ≥ 2
To do this, we take it one at a time
5x + 8 > 23
Subtract 8 from both sides
5x + 8 - 8 > 23 - 8
5x > 15
Divide both sides by 5
(5x/5) > (15/5)
x > 3
-4x + 6 ≥ 2
Subtract 6 from both sides
-4x + 6 - 6 ≥ 2 - 6
-4x ≥ -4
Divide both sides by -4 (Note that dividing both sides of an inequality equation by a negative number changes the direction of the inequality sign)
(-4x/-4) ≤ (-4/-4)
x ≤ 1
So, the solution is
x > 3 OR x ≤ 1
x ≤ 1 OR x > 3
To put it in interval form (bracket form), we must note that 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 ≤ 1 means that x is all the numbers starting from 1 to all the numbers less than 1
x ≤ 1 = (-∞, 1]
x > 3 means that x is all the numbers more than 3
x > 3 = (3, ∞)
x ≤ 1 OR x > 3 = (-∞, 1] U (3, ∞)
H