Tuesday, May 1, 2012

Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 78

Solve the inequality |0.5x3.5|+0.20.6.


|0.5x3.5|+0.20.6|0.5x3.5|0.4


The absolute value inequality is rewritten as

0.5x3.50.4 or 0.5x3.50.4,

because 0.5x3.5 must represent a number that is more than 0.4 units from on either side of the number line. We can solve the compound inequality.


0.5x3.50.4or0.5x3.50.45x354or5x354Multiply each side by 105x39or5x31Add each side by 35x395orx315


The solution set is (315,395).

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