expression **$K$** and your boundary **$a$**. 2. **Set up** the compound inequality: **$-a < K < a$**. 3. **Solve** for the variable by getting it alone in the middle. **Test-style question:** Solve the inequality $|2x - 1| < 9$. **Solution:** 1. **Apply the rule:** We sandwich the expression $2x - 1$ between $-9$ and $9$. $$ -9 < 2x - 1 < 9 $$ 2. **Isolate the x-term:** Add 1 to all three parts of the inequality to get the $2x$ term by itself. $$ -9 + 1 < 2x - 1 + 1 < 9 + 1 $$ $$ -8 < 2x < 10 $$ 3. **Solve for x:** Divide all three parts by 2. $$ \frac{-8}{2} < \frac{2x}{2} < \frac{10}{2} $$ $$ -4 < x < 5 $$ The solution is all numbers strictly between -4 and 5. **Common mistake tip:** A super common mistake is forgetting to apply an operation to **all three parts** of the inequality. When you add or subtract something, make sure you do it to the left side, the middle, *and* the right side to keep it balanced!23:T5c9,{"@context":"https://schema.org","@type":"LearningResource","@id":"https://pengi.ai/learn/skills/solving-less-than-absolute-value-inequalities-68226149-e9e8-4c34-b296-09d0eb8012ff#skill","name":"Solving 'Less Than' Absolute-Value Inequalities","headline":"Solving 'Less Than' Absolute-Value Inequalities","description":"Solving 'Less Than' Absolute-Value Inequalities is a skill on Pengi from Lesson 91: Solving Absolute-Value Inequalities in Saxon Algebra 1.","image":"https://syllabus-cdn.nanci.ai/syllabus_image/anonymous-1755038841773-w064geb1.jpg","educationalLevel":"Grade 9","about":"math","learningResourceType":"Skill","isAccessibleForFree":true,"inLanguage":"en","teaches":"Solving 'Less Than' Absolute-Value Inequalities","publisher":{"@type":"Organization","name":"Pengi","url":"https://pengi.ai"},"isPartOf":{"@type":"LearningResource","@id":"https://pengi.ai/learn/lesson-91-solving-absolute-value-inequalities-5593ac1f-778d-4368-a258-9842fcd7cab3#lesson","name":"Lesson 91: Solving Absolute-Value Inequalities","url":"https://pengi.ai/learn/lesson-91-solving-absolute-value-inequalities-5593ac1f-7