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Pearson Algebra 2 Common Core, 2011 View details

6. Absolute Value Equations and Inequalities

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Exercise 28 Page 46

Absolute values are always non-negative.

Solution Set: No solution.
Graph:

Practice makes perfect

Before we can solve this inequality, we need to isolate the absolute value expression using the Properties of Inequality.

1/4|x-3|+2<1

SubIneq

LHS-2

1/4|x-3|< -1

MultIneq

LHS* 4 < RHS * 4

|x-3| < -4

All absolute value expressions are greater than or equal to zero. It follows then that no absolute value expressions can be less than or equal to a negative number. |x-3|≥ 0 ⇒ |x-3| ≮ - 4 This means there is no value of t that will satisfy the inequality. Therefore, there is no solution. We can represent this graphically on a number line by showing that no values are included in the solution set, so no values are shaded.