|t–4|≤2
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.

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We begin by solving the absolute value inequality:

\[
|t - 4| \leq 2
\]

This inequality means that the expression inside the absolute value, \( t - 4 \), lies within 2 units of 0. To remove the absolute value, we rewrite the inequality as a compound inequality:

\[
-2 \leq t - 4 \leq 2
\]

Now, solve for \( t \) by adding 4 to all three parts of the inequality:

\[
-2 + 4 \leq t - 4 + 4 \leq 2 + 4
\]

\[
2 \leq t \leq 6
\]

Thus, the solution is:

\[
2 \leq t \leq 6
\]

This is the compound inequality that describes the solution set.

Would you like more details on solving absolute value inequalities?

Here are 5 related questions to expand your understanding:
1. How would the solution change if the inequality was \( |t - 4| \geq 2 \)?
2. What are the steps to solve an inequality with a negative absolute value, such as \( |t - 4| \leq -2 \)?
3. How do you solve absolute value inequalities with a variable on both sides?
4. Can you solve \( |2t - 1| \leq 3 \)? What does the compound inequality look like?
5. How do you graph the solution \( 2 \leq t \leq 6 \) on a number line?

**Tip**: Always isolate the absolute value term before solving these inequalities.

|t–4|≤2. 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 |t–4|≤2, leading to the compound inequality 2 ≤ t ≤ 6. This problem covers absolute value inequalities and compound inequalities, with a step-by-step solution. Ideal for students in Grades 8-10.

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