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McGraw Hill Glencoe Algebra 1, 2012 View details

5. Inequalities Involving Absolute Value

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Exercise 18 Page 314

Absolute values are always non-negative.

Solution Set: {v|v is a real number.}
Graph:

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All absolute value expressions are greater than or equal to zero. It follows then that any absolute value expression is greater than all negative numbers. |5v+3|≥ 0 ⇒ |5v+3|>- 9 This means any value of v will satisfy the inequality. Therefore, there are infinitely many solutions, and the solution set is the set of all real numbers. We can represent this graphically on a number line by showing that all values are included in the solution set, so all values are shaded.