Question

Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.−5x+3≤−47 or −5x+3<−57

Answer 1

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)

`-5x+3\leq-47`

Isolating x:

`\begin{gathered} -5x+3\leq-47 \\ -5x\leq-47-3 \\ -5x\leq-50(\cdot-1) \\ 5x\ge50 \\ x\ge(50)/(5) \\ x\ge10 \end{gathered}`

(B)

`\begin{gathered} -5x+3<-57 \\ -5x<-57-3 \\ -5x<-60(\cdot-1) \\ 5x>60 \\ x>(60)/(5) \\ x>12 \end{gathered}`

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: