Chapter 3.3, Problem 3E

a)

To determine

To find: ABASIC program to solve the equation of form$A\left|x\right|+B=C$ and to use it to solve the equation$\left|x\right|+8=10$ .

Answer to Problem 3E

Output: Solution of the given equation is$x=2$ and$x=-2$ .

Explanation of Solution

Given information: A linear equation of form$A\left|x\right|+B=C$ and another equation$\left|x\right|+8=10$ to be solved for unknown variable x , using appropriate BASIC program.

Concept used: Use different syntax that are used to PRINT, INPUT and do other operations to solve a linear equation in one variable, while writing required BASIC program.

BASIC program to solve given equation of form$A\left|x\right|+B=C$ is:

10    PRINT “Program to solve equation$A\left|x\right|+B=C$ ”;

20    PRINT “Enter values of A , B , and C :“;

30    LET x =0;

40    INPUT A , B , C ;

50   $A*x=B-C$ ;

60   $x=\frac{\left(B-C\right)}{A}$

70    PRINT “Solution of given equation is$x=$ ”;$x=\frac{\left(B-C\right)}{A}$ ;”and$x=-\frac{\left(B-C\right)}{A}$ ; 80    IF A=0 THEN 90;

90    PRINT “Given equation has NO SOLUTION”

100    END

Output: Program to solve equation$A\left|x\right|+B=C$

Enter values of A , B , and C : 1 8 10

Solution of the given equation is x = 2 and x = -2

Here line 10-20, print different messages. Line 40 asks the values of constants and coefficients used in the equation. Lines 50-60 solve the equation for unknown variable x . LINE 70 returns the result of the equation. And line 90 implies the condition for equation having NO SOLUTION.

Get the solution of the given equation$\left|x\right|+8=10$ , by putting following values, while running above program.

  $A=1,B=8,C=10$

Conclusion: On running the above program, the solution of the equation$\left|x\right|+8=10$ is calculated as$x=2$ and$x=-2$ .

b)

To determine

To find: A modified BASIC program to solve the equation of form$A\left|x\right|+B=C$ and to use it to solve the equation$\left|x\right|+10=8$ .

Answer to Problem 3E

Output of the above program is NO SOLUTION.

Explanation of Solution

Given information: A linear equation of form$A\left|x\right|+B=C$ and another equation$\left|x\right|+10=8$ to be solved for unknown variable x , using appropriate BASIC program.

Concept used: Use different syntax that are used to PRINT, INPUT and do other operations to solve a linear equation in one variable, while writing required BASIC program.

BASIC program to solve given equation of form$A\left|x\right|+B=C$ is:

10    PRINT “Program to solve equation$A\left|x\right|+B=C$ ”;

20    PRINT “Enter values of A , B , and C .“;

30    LET x = 0;

40    INPUT A , B , C ;

50   $A*x=B-C$ ;

60   $x=\frac{\left(B-C\right)}{A}$ ;

70    PRINT “Solution of given equation is x=”;$x=\frac{\left(B-C\right)}{A}$ ;”and x=”;$x=-\frac{\left(B-C\right)}{A}$ ;

80    IF A = 0 THEN 90;

90   PRINT “Given equation has NO SOLUTION.”

100    END

Output: Program to solve equation$A\left|x\right|+B=C$

Enter values of A , B , and C : 1 10 8

Given equation has NO SOLUTION.

Here line 10-20, print different messages. Line 40 asks the values of constants and coefficients used in the equation. Lines 50-60 solve the equation for unknown variable x . LINE 70 returns the result of the equation. And line 90 implies the condition for equation having NO SOLUTION.

Get the solution of the given equation$\left|x\right|+10=8$ , by putting following values, while running above program.

  $A=1,B=10,C=8$

Conclusion: On running the above program, the solution of the equation$\left|x\right|+10=8$ is calculated as NO SOLUTION,.

c)

To determine

To find: A BASIC program to solve the equation of form$A\left|x\right|+B=C$ and to use it to solve

the equation$6\left|x\right|+2=5$ .

Answer to Problem 3E

Solution of the given equation is$x=\frac{1}{2}$ and$x=-\frac{1}{2}$ .

Explanation of Solution

Given information: A linear equation of form$A\left|x\right|+B=C$ and another equation$6\left|x\right|+2=5$ to be solved for unknown variable x , using appropriate BASIC program.

Concept used: Use different syntax that are used to PRINT, INPUT and do other operations to solve a linear equation in one variable, while writing required BASIC program.

BASIC program to solve given equation of form$A\left|x\right|+B=C$ is:

10    PRINT “Program to solve equation$A\left|x\right|+B=C$ ”;

20    PRINT “Enter values of A , B , and C .“;

30    LET x=0;

40    INPUT A , B , C ;

50   $A*x=B-C$ ;

60   $x=\frac{\left(B-C\right)}{A}$ ;

70    PRINT “Solution of given equation is x=”;$x=\frac{\left(B-C\right)}{A}$ ;”and x =”;$x=-\frac{\left(B-C\right)}{A}$;

80    IF A=0 THEN 90;

90    PRINT “Given equation has NO SOLUTION”

100    END

Output: Program to solve equation$A\left|x\right|+B=C$

Enter values of A , B , and C : 6 2 5

Solution of the given equation is x = 0.5 and x = - 0.5

Here line 10-20, print different messages. Line 40 asks the values of constants and coefficients used in the equation. Lines 50-60 solve the equation for unknown variable x . LINE 70 returns the result of the equation. And line 90 implies the condition for equation having NO SOLUTION.

Get the solution of the given equation$6\left|x\right|+2=5$ , by putting following values, while running above program.

  $A=6,B=2,C=5$

Conclusion: On running the above program, the solution of the equation$6\left|x\right|+2=5$ is calculated as$x=\frac{1}{2}$ and$x=-\frac{1}{2}$ .