document.write( "Question 257610: What is the least value of y that satisfies the following inequality?\r
\n" ); document.write( "\n" ); document.write( "|4+x|+|5+y|≤100 \n" ); document.write( "

Algebra.Com's Answer #190882 by drk(1908) $\"\"$ $\"About$

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WIth these absolute values we must start with 4 inequalities. here are the four:
\n" ); document.write( "(i) $\"%284%2Bx%29+%2B+%285%2By%29+%3C=+100\"$
\n" ); document.write( "(ii) $\"%284%2Bx%29+-+%285%2By%29+%3C=100\"$
\n" ); document.write( "(iii) $\"-%284%2Bx%29+%2B+%285%2By%29+%3C=100\"$
\n" ); document.write( "(iv) $\"-%284%2Bx%29+-+%285%2By%29+%3C=100\"$
\n" ); document.write( "--
\n" ); document.write( "we can solve each of these for y as
\n" ); document.write( "(i) becomes (v) $\"y+%3C=+91-x\"$
\n" ); document.write( "(ii) becomes (vi) $\"y+%3E=+x-101\"$
\n" ); document.write( "(iii) becomes (vii) $\"y%3C=+x+%2B+99\"$
\n" ); document.write( "(iv) becomes (viii) $\"y%3E=+-x+-109\"$
\n" ); document.write( "--
\n" ); document.write( "Graphing them creates a quadrilateral. We now graph these and look for the minimum y crossing points. This occurs when (vi) crosses over (viii). We get
\n" ); document.write( " $\"y+%3E=+x-101\"$
\n" ); document.write( " $\"y%3E=+-x+-109\"$
\n" ); document.write( "adding down, the x's drop out and we get
\n" ); document.write( " $\"2y+%3E=+-210\"$
\n" ); document.write( "and then
\n" ); document.write( " $\"y+%3E=+-105\"$
\n" ); document.write( "So, the minimum value of y is -105. \n" ); document.write( "

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