Lesson summary for Inequalities Involving Absolute Value
- Absolute value inequalities are mathematical expressions where the absolute value of a variable or expression is compared to a constant.
- The absolute value of a number represents its distance from zero on a number line, always yielding a non-negative result.
- Solving Absolute Value Inequalities
- Inequalities of the Form $ |x – a| < b $:
- Write the compound inequality without the absolute value: $( -b < x – a < b )$.
- Solve for (x) by isolating it in the middle: $( a – b < x < a + b)$.
- Inequalities of the Form $( |x – a| \leq b)$
- Write the compound inequality without the absolute value: $( -b \leq x – a \leq b)$.
- Solve for (x) by isolating it in the middle: $( a – b \leq x \leq a + b)$.
- Inequalities of the Form $( |x – a| > b)$
- Break it into two inequalities: $( x – a > b)$ or $( x – a < -b)$.
- Inequalities of the Form $ |x – a| \geq b$
- Break it into two inequalities: $( x – a \geq b)$ or $( x – a \leq -b)$.