document.write( "Question 68439: Solve the following problem: |2x-7|-5=4 \r
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Algebra.Com's Answer #48771 by rmromero(383)\"\" \"About 
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|2x-7|-5=4
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Add 5 both sides
\n" ); document.write( " |2x - 7| = 9
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This Equation is equivalent to a combined equation containing or , a disjunction. THe equation has two solutions.
\n" ); document.write( "2x - 7 = 9 or 2x - 7 = -9
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Solve for x:
\n" ); document.write( "1. 2x - 7 = 9
\n" ); document.write( " 2x = 16
\n" ); document.write( " x = 8
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\n" ); document.write( "2. 2x - 7 = -9
\n" ); document.write( " 2x = -2
\n" ); document.write( " x = -1
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\n" ); document.write( "Checking
\n" ); document.write( "|2x - 7| - 5 = 4
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When x = 8
\n" ); document.write( "|2(8) - 7| - 5 = 4
\n" ); document.write( "|9| - 5 = 4
\n" ); document.write( "9 - 5 = 4
\n" ); document.write( "4 = 4 ---> true
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\n" ); document.write( "when x = -1
\n" ); document.write( "|2x -7| - 5 = 4
\n" ); document.write( "|2(-1)- 7| - 5 = 4
\n" ); document.write( "|-2 - 9| - 5 = 4
\n" ); document.write( "|-9| - 5 = 4
\n" ); document.write( "9 - 5 = 4
\n" ); document.write( "4 = 4 ---> True\r
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It is important to check your solution in the original equation.
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Since both values makes the |2x-7|-5 = 4 true, therefore, the solution set is {8, -1}
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