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Solve for $d$ . $|d - 5| \geq 5$ Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$ . Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

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Solve absolute value inequalities

Full solution

Q. Solve for

d

.

|d - 5| \geq 5

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Absolute Value Inequality: We have the inequality $|d - 5| \geq 5$ . The absolute value inequality means that the expression inside the absolute value, $d - 5$ , can either be greater than or equal to $5$ or less than or equal to $-5$ .
Case $1$ : $d - 5 \geq 5$ : First, let's consider the case where $d - 5$ is greater than or equal to $5$ : $d - 5 \geq 5$ Now, we add $5$ to both sides of the inequality to solve for $d$ : $d - 5 + 5 \geq 5 + 5$ $d \geq 10$
Case $2$ : $d - 5 \leq -5$ : Next, let's consider the case where $d - 5$ is less than or equal to $-5$ : $d - 5 \leq -5$ Again, we add $5$ to both sides of the inequality to solve for $d$ : $d - 5 + 5 \leq -5 + 5$ $d \leq 0$
Compound Inequality: Combining both cases into a compound inequality, we get: $\newline$ $d \leq 0$ or $d \geq 10$ $\newline$ This is the solution to the given inequality $|d - 5| \geq 5$ .

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