Solve 3x - 4 ≀ 2 or 2x + 11 β‰₯ -1

Accepted Solution

Answer:The solution is all real numbersStep-by-step explanation:we have the system of inequalities[tex]3x-4\leq 2[/tex] -----> inequality Aor[tex]2x+11\geq -1[/tex] ----> inequality Bstep 1Solve inequality AAdds 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 2Solve inequality BSubtract 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 3Find out the solution of the system of inequalitiesThe 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,∞) βˆͺ (-∞,2]=(-∞,∞)The solution is all real numbers