document.write( "Question 1196404: |3x-6| >9 Solve each absolute value inequality. Graph the solution.\r
\n" ); document.write( "\n" ); document.write( "The bigger sign actually has a line immediately under it.\r
\n" ); document.write( "\n" ); document.write( "First i added 6 to -6 and to 9 after I got 15 from 9+6 I didn’t know what to do I need help understanding the process of solving the question. Please and thank you. \n" ); document.write( "
Algebra.Com's Answer #829239 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Rule to write down in your notebook:
\n" ); document.write( "If |A| ≥ B, then either A ≥ B or A ≤ -B\r
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\n" ); document.write( "\n" ); document.write( "Example:
\n" ); document.write( "|x| ≥ 12 means x ≥ 12 or x ≤ -12
\n" ); document.write( "|x| represents the distance from x to 0 on the number line. We want the distance to be 12 or larger. So that places us in the interval x ≥ 12 or x ≤ -12
\n" ); document.write( "I strongly recommend drawing out a number line to see what's going on.\r
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\n" ); document.write( "\n" ); document.write( "Anyways, onto the problem at hand:
\n" ); document.write( "|3x-6| ≥ 9
\n" ); document.write( "3x-6 ≥ 9 or 3x-6 ≤ -9 ..... use the rule mentioned above
\n" ); document.write( "3x ≥ 9+6 or 3x ≤ -9+6
\n" ); document.write( "3x ≥ 15 or 3x ≤ -3
\n" ); document.write( "x ≥ 15/3 or x ≤ -3/3
\n" ); document.write( "x ≥ 5 or x ≤ -1
\n" ); document.write( "x ≤ -1 or x ≥ 5\r
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\n" ); document.write( "\n" ); document.write( "x ≤ -1 turned into interval notation is (-∞, -1]
\n" ); document.write( "x ≥ 5 turned into interval notation is [5, ∞)
\n" ); document.write( "The entire solution set in interval notation is (-∞, -1] U [5, ∞) where the U symbol is the union operator.\r
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\n" ); document.write( "\n" ); document.write( "To graph this, we'll have closed filled in circles at -1 and 5
\n" ); document.write( "The closed circles signal to the reader \" include this endpoint in the shaded solution set\".
\n" ); document.write( "Then we shade everywhere but the region between the closed endpoints
\n" ); document.write( "We shade to the left of -1; and to the right of 5
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\n" ); document.write( "\n" ); document.write( "If you were to pick any value from the shaded region (say x=7), then it makes the original inequality true
\n" ); document.write( "|3x-6| ≥ 9
\n" ); document.write( "|3*7-6| ≥ 9
\n" ); document.write( "|21-6| ≥ 9
\n" ); document.write( "|15| ≥ 9
\n" ); document.write( "15 ≥ 9
\n" ); document.write( "The last inequality is true, so the original inequality is true for x = 7.
\n" ); document.write( "Try out other x values from the shaded regions to help partially confirm the answer.
\n" ); document.write( "Also, try out values from the non-shaded region to see they make the inequality false.\r
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\n" ); document.write( "\n" ); document.write( "Side note: The keyword \"or\" is used (not \"and\") when joining the intervals x ≤ -1 or x ≥ 5. This is to say x could be in either interval.
\n" ); document.write( "We can't say x ≤ -1 and x ≥ 5 since x cannot be in both intervals at once.
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