|7d|≤7
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.

To solve the inequality \(|7d| \leq 7\), we need to break it down and remove the absolute value. This results in a compound inequality:

\[
-7 \leq 7d \leq 7
\]

Now, divide the entire inequality by 7 to isolate \(d\):

\[
\frac{-7}{7} \leq d \leq \frac{7}{7}
\]

This simplifies to:

\[
-1 \leq d \leq 1
\]

Thus, the compound inequality is:

\[
-1 \leq d \leq 1
\]

Would you like further details or explanations? Here are 5 related questions:

1. How do you solve absolute value inequalities in general?
2. Can the solution to an absolute value inequality ever be an "or" compound inequality?
3. What happens if the inequality is \(|7d| > 7\) instead of \(|7d| \leq 7\)?
4. How does solving inequalities differ when the absolute value is less than or equal versus greater than or equal?
5. What are the steps to graph the inequality \(-1 \leq d \leq 1\) on a number line?

**Tip:** When dealing with absolute value inequalities, always consider whether the solution results in an "and" or "or" compound inequality.

|7d| ≤ 7. 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.

Learn how to solve the absolute value inequality |7d| ≤ 7 by breaking it into a compound inequality. This step-by-step solution explains key concepts, such as absolute value, inequalities, and proper simplification methods. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation