Chapter 1.4, Problem 52E

To determine

Tofind:the variable $a,b,c\text{ and }d$ than can be filled in blank.

Answer to Problem 52E

  $\left|x-b\right|=d$ .

Explanation of Solution

Given:

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Concept used:

Absolute value or modulus of a real number $x$ ,denoted that $\left|x\right|$ , is the non-negative value of $x$ without regard to its sign.

Mathematically,

  $\left|x\right|=x.$

If domain $x$ is positive.

  $\left|x\right|=-x.$

If domain $x$ is negative.

Calculation:

In solving absolute value equations, remember that:

  $\left|ax+b\right|=\left|c\right|$ provided that $c\ge 0$ will be either be:

  $ax+b=c\text{ or }ax+b=-c$ .

Note that when $c<0$ , the equation has no solution because, absolute values are always positive.

In graphing the solutions, place a closed dot on each of the solutions of the equation.

Based on the graph it is noticed that each solution, $a\text{ and }c$ , is $d$ units from $b$ , therefore, the grpah’s equation should be $\left|x-b\right|=d$ .

Hence, $\left|x-b\right|=d$ .