Solve for d. |d - 5| ≥ 5 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form. ______

Absolute Value Inequality: We have the inequality |d - 5| ≥ 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 ≥ 5: First, let's consider the case where d - 5 is greater than or equal to 5: d - 5 ≥ 5 Now, we add 5 to both sides of the inequality to solve for d: d - 5 + 5 ≥ 5 + 5 d ≥ 10Case 2: d - 5 ≤ -5: Next, let's consider the case where d - 5 is less than or equal to -5: d - 5 ≤ -5 Again, we add 5 to both sides of the inequality to solve for d: d - 5 + 5 ≤ -5 + 5 d ≤ 0Compound Inequality: Combining both cases into a compound inequality, we get: d ≤ 0 or d ≥ 10 This is the solution to the given inequality |d - 5| ≥ 5.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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. $\newline$ ______

View step-by-step help

Home

Math Problems

Algebra 2

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

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 $|d - 5| \geq 5$ .