QuestionSimplify the expression $\frac{15-z}{|15-z|}$ for the case when $z<15$ .

Studdy Solution

STEP 1

Assumptions1. The expression is $\frac{15-z}{|15-z|}$ . The condition is $z<15$

STEP 2

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|15-z|$ can be either $(15-z)$ or $-(15-z)$ , depending on whether $15-z$ is positive or negative.

STEP 3

Given the condition $z<15$ , we know that $15-z$ is positive. Therefore, $|15-z|$ simplifies to $(15-z)$ .

STEP 4

Substitute $(15-z)$ for $|15-z|$ in the original expression.
$\frac{15-z}{(15-z)}$

STEP 5

implify the expression. Any number divided by itself is1, so the expression simplifies to1.
$\frac{15-z}{(15-z)} =1$ The simplified expression without absolute value bars is1.

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