Which of the following is the correct graph of the solution to the inequality-18>-5x+2>-48

Accepted Solution

Answer:Step-by-step explanation:we have[tex]18 > -5x+2 > -48[/tex]This is a compound inequalityRemember thatA compound inequality i can divide in a system of two inequalitiesso[tex]18 > -5x+2[/tex] -----> inequality A[tex]-5x+2 > -48[/tex] ---> inequality Bstep 1Solve the inequality A[tex]18 > -5x+2[/tex]Multiply by -1 both sides[tex]-18< 5x-2[/tex][tex]-18+2< 5x[/tex][tex]-16< 5x[/tex]Divide by 5 both sides[tex]-3.2< x[/tex]Rewrite[tex]x > -3.2[/tex]The solution of the inequality A is the interval ----> (-3.2,∞)step 2Solve the inequality B[tex]-5x+2 > -48[/tex]Multiply by -1 both sides[tex]5x-2 < 48[/tex][tex]5x < 48+2[/tex][tex]5x < 50[/tex]Divide by 5 both sides[tex]x < 10[/tex]The solution of the inequality B is the interval ----> (-∞, 10)step 3Find the solution of the compound inequality(-3.2,∞) ∩ (-∞, 10)=(-3.2,10)All real numbers greater than -3.2 and less than 10The graph in the attached figure