Which of the following is a solution of the compound inequality?
3x + 8 < 2 or x + 12 > 2 - x
To find the solution to the compound inequality 3x + 8 < 2 or x + 12 > 2 - x, we will split it into two separate inequalities and solve each one individually.
First, let's solve the inequality 3x + 8 < 2:
1. Subtract 8 from both sides:
3x + 8 - 8 < 2 - 8
3x < -6
2. Divide both sides by 3 to isolate x:
(3x)/3 < (-6)/3
x < -2
So, the first inequality gives us x < -2.
Now, let's solve the inequality x + 12 > 2 - x:
1. Add x to both sides:
x + x + 12 > 2 - x + x
2x + 12 > 2
2. Subtract 12 from both sides:
2x + 12 - 12 > 2 - 12
2x > -10
3. Divide both sides by 2 to isolate x:
(2x)/2 > (-10)/2
x > -5
So, the second inequality gives us x > -5.
Combining the solutions from both inequalities, we have:
x < -2 or x > -5
This means that x can be any value less than -2 or any value greater than -5.