a. Which of the following represents all values of x whose distance from 7 is less than 8? Select all that apply.

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### Educational Assessment: Absolute Value Inequalities

This section explores the concept of absolute value inequalities, focusing on finding the range of values that satisfy given conditions regarding distances from a specified point.

#### a. Distance from 7 Less Than 8
Identify all values of \( x \) such that the distance from 7 is less than 8. Select all statements that correctly represent this condition:

- \(\lvert x - 7 \rvert \leq 8\)
- \(\lvert x - 8 \rvert < 7\) **(Selected)**
- \(\lvert x - 7 \rvert < 8\)
- \(\lvert x - 8 \rvert > 7\)

#### b. Distance from 3 More Than 0.8
Determine all values of \( r \) such that their distance from 3 is more than 0.8. Choose all applicable options:

- \(\lvert r - 3 \rvert > 0.8\)
- \(\lvert r - 0.8 \rvert > 3\)
- \(\lvert r - 3 \rvert < 0.8\)
- \(\lvert r - 0.8 \rvert < 0.8\)

#### c. Distance from -5 No More Than 3.5
Identify all possible values of \( s \) with a distance from -5 no more than 3.5. Select all valid conditions:

- \(\lvert s + 5 \rvert < 3.5\) **(Selected)**
- \(\lvert s + 5 \rvert \leq 3.5\)
- \(\lvert s - 5 \rvert < 3.5\)
- \(\lvert s - 5 \rvert \leq 3.5\)

**Note:** Each question has boxes labeled Box 1, Box 2, and Box 3, inviting the selection of all correct answers. 

This exercise aids in understanding how absolute values can represent distances on a number line and solving inequalities involving these distances.
Transcribed Image Text:### Educational Assessment: Absolute Value Inequalities This section explores the concept of absolute value inequalities, focusing on finding the range of values that satisfy given conditions regarding distances from a specified point. #### a. Distance from 7 Less Than 8 Identify all values of \( x \) such that the distance from 7 is less than 8. Select all statements that correctly represent this condition: - \(\lvert x - 7 \rvert \leq 8\) - \(\lvert x - 8 \rvert < 7\) **(Selected)** - \(\lvert x - 7 \rvert < 8\) - \(\lvert x - 8 \rvert > 7\) #### b. Distance from 3 More Than 0.8 Determine all values of \( r \) such that their distance from 3 is more than 0.8. Choose all applicable options: - \(\lvert r - 3 \rvert > 0.8\) - \(\lvert r - 0.8 \rvert > 3\) - \(\lvert r - 3 \rvert < 0.8\) - \(\lvert r - 0.8 \rvert < 0.8\) #### c. Distance from -5 No More Than 3.5 Identify all possible values of \( s \) with a distance from -5 no more than 3.5. Select all valid conditions: - \(\lvert s + 5 \rvert < 3.5\) **(Selected)** - \(\lvert s + 5 \rvert \leq 3.5\) - \(\lvert s - 5 \rvert < 3.5\) - \(\lvert s - 5 \rvert \leq 3.5\) **Note:** Each question has boxes labeled Box 1, Box 2, and Box 3, inviting the selection of all correct answers. This exercise aids in understanding how absolute values can represent distances on a number line and solving inequalities involving these distances.
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