Answer
a) x > 2 OR x < -3
b) x < -4 OR x ≥ -5
Step-by-step explanation
The compound inequalities to be solved and graphed include
a) (5x + 1) > 11 OR (x - 1) < -4
b) (-5x) > 20 OR (x - 2) ≥ -7
The first step is to solve these expressions
a) (5x + 1) > 11 OR (x - 1) < -4
5x + 1 > 11
Subtract 1 from both sides
5x + 1 - 1 > 11 - 1
5x > 10
Divide both sides by 5
(5x/5) > (10/5)
x > 2
OR
x - 1 < -4
Add 1 to both sides
x - 1 + 1 < -4 + 1
x < -3
So, the solution for this is x > 2 OR x < -3
b) (-5x) > 20 OR (x - 2) ≥ -7
(-5x) > 20
Divide both sides by -5
Note that dividing both sides by a negative number causes the inequality sign to change
(-5x/-5) < (20/-5)
x < -4
OR
(x - 2) ≥ -7
Add 2 to both sides
x - 2 + 2 ≥ -7 + 2
x ≥ -5
So, the solution for this is x < -4 OR x ≥ -5
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.