Chapter 1.5, Problem 69E

To determine

The value of $x$ for value of expression greater than $0$ .

Answer to Problem 69E

The value of $x$ is any integer greater than $10$ or less than $-10$ .

Explanation of Solution

Given information:

The following expression:

$-10+\left|x\right|$

Calculation: To solve the given expression, so that its value is greater than $0$ , the value of $x$ should be greater than $10$ or less than $-10$ . Consider two cases:

Case 1: $x$ is positive. The equation can be written as-

$-10+x$

Since the numbers have an opposite sign, they will be subtracted and the sign of the greater number will be assigned to the answer. The equation will yield a positive value greater than $0$ when $x$ has a value greater than $10$ . If the value of $x$ is equal to $10$ , the equation will yield $0$ .

Example:

$-10+12=2$

Case 2: $x$ is negative. The equation can be written as-

$-10+\left|-x\right|$

Since the absolute value of $-x$ is $x$ , any negative value less than $10$ can be considered since an absolute value is used.

Example:

$-10+\left|-15\right|=-10+15=5$

Conclusion: In case 1, $x$ has a positive value greater than $10$ and in case 2, $x$ has a negative value less than $-10$