Answer:
The solution is all real numbers
Step-by-step explanation:
we have the system of inequalities
[tex]3x-4\leq 2[/tex] -----> inequality A
or
[tex]2x+11\geq -1[/tex] ----> inequality B
step 1
Solve inequality A
Adds 4 both sides
[tex]3x\leq 2+4[/tex]
[tex]3x\leq 6[/tex]
Divide by 3 both sides
[tex]x\leq 2[/tex]
The solution is the interval ----> (-∞,2]
step 2
Solve inequality B
Subtract 11 both sides
[tex]2x\geq -1-11[/tex]
[tex]2x\geq -12[/tex]
Divide by 2 both sides
[tex]x\geq -6[/tex]
The solution is the interval ----> [-6,∞)
step 3
Find out the solution of the system of inequalities
The solution of the system is equal to the solution inequality A plus the solution of the inequality B (because the system has included the word "or")
so
[-6,∞) ∪ (-∞,2]=(-∞,∞)
The solution is all real numbers
