Chapter 2.5, Problem 6E

To determine

Torun the given program to solve given inequality.

Explanation of Solution

Given:

The given inequality is $-4\left|x-1\right|>-8$

Calculation:

The given inequality can be rewritten as-

  $\begin{array}{l}-4\left|x-1\right|>-8\\ 4\left|x-1\right|<8\\ \left|x-1\right|<2\end{array}$

The following is the givenBASICProgram-

10 PRINT “THIS PROGRAM WILL SOLVE INEQUALITY”
20 PRINT “OF THE FORM ABS (A*X+B) SIGN C”
30PRINT “WITH A NOT ZERO, THE SIGN IS <OR >”.
40 INPUT “ENTER A, B, C, AND THE SIGN: “A, B, C, S$
50 IF S$=”<” AND C<=0 THEN 60
55 PRINT “SOLUTION SET CONSISTS OF X SUCH THAT”
60 IF S$=”<” AND A>0 AND C>0 THEN PRINT
       (-C-B)/A;”<XAND X><”;(C-B)/A
70 IF S$=”<” AND A<0 AND C>0 THEN PRINT
       (-C-B)/A;”<XAND X><”;(-C-B)/A
80 IF S$=”>” AND A>0 AND C>=0 THEN PRINT
“X<”;(-C-B)/A;” OR X>”;(C-B)/A
90 IF S$=”>” AND A<0 AND C>=0 THEN PRINT
       “X<”;(C-B)/A;” OR X>”;(-C-B)/A
100 IF S$=”>” AND C>0 THEN PRINT
        “X IS ANY REAL NUMBER”
110 IF S$=”<” AND C<=0 THEN PRINT
        “THERE IS NO SOLUTION”
120 END

DRY RUN of the program:-

SAMPLE OUTPUT:

THIS PROGRAM WILL SOLVE INEQUALITY

OF THE FORM ABS (A*X+B) SIGN C

WITH A NOT ZERO, THE SIGN IS< OR >

ENTER A, B, C, AND THE SIGN: “A, B, C, S

  $A=1,B=-1,C=2,S=<$

SOLUTION SET CONSISTS OF X SUCH THAT

  $X<3$ AND $X>-1$