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Chapter 1: Q55. (page 32)

For Exercises 55-58, consider the equation x+1+2=x+4.

55. To solve this equation we must consider the case where x+4鈮�0and the case where x+4<0. Write the equations for each of these cases.

Short Answer

Expert verified

When x+4鈮�0 given equation becomes x+1+2=x+4

When x+4<0 given equation becomes x+1+2=-x+4

Step by step solution

01

- Define absolute value

For a real number a, a=a if a鈮�0 and a=-a if a<0

02

- Case when x+4≥0

Using definition of absolute value, x+4=x+4 when x+4鈮�0

Thus, given equation becomes x+1+2=x+4

03

- Case when x+4<0

Using definition of absolute value, x+4=-x+4when x+4<0

Thus, given equation becomes x+1+2=-x+4

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