Compound inequality with "Or” indicates that, if one statement is true, the entire compound sentence is true.
1) So, let's evaluate each inequality:
(A)
[tex]-5x+3\leq-47[/tex]Isolating x:
[tex]\begin{gathered} -5x+3\leq-47 \\ -5x\leq-47-3 \\ -5x\leq-50(\cdot-1) \\ 5x\ge50 \\ x\ge\frac{50}{5} \\ x\ge10 \end{gathered}[/tex](B)
[tex]\begin{gathered} -5x+3<-57 \\ -5x<-57-3 \\ -5x<-60(\cdot-1) \\ 5x>60 \\ x>\frac{60}{5} \\ x>12 \end{gathered}[/tex]As we can see, the solution of equation A contains also the solution of equation B.
Also, in "Or” inequalities, it is only necessary that one statement is true. So, if statement A is true, the inequality is solved.
Answer:
{x ∈ R/x ≥ 10} or [10,∞)
Graph:
