Solving Equations with absolute value and less than inequalities

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Solving Equations with absolute value and less
than inequalities

• Section 1-7 Algebra II
• R. Conyer

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EXAMPLE ONE X lt 10 If the
absolute value equation contains the
less than inequality then you will set up
the following expression. -10 lt X
lt 10 Solution Step One Place the
negative of the number on the left. Place the
less than symbol next. Put X in the middle.
Place the less than symbol next. Put the
original number on the right.
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EXAMPLE TWO X - 6 lt 8 If
the absolute value equation contains
the less than inequality then you will
set up the following expression. -8
lt X - 6 lt 8 Step one Place the
negative of the number on the left. Place the
less than symbol next. Put X - 6 in the middle.
Place the less than symbol next. Put the
original number on the right.
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-8 lt X - 6 lt 8 Step Two Add six to
three positions in the expression. -8 lt X -
6 lt 8 6 6 6 -2
0 14 SOLUTION - 2 lt x lt 14
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EXAMPLE THREE 4X 11 lt 19 If the
absolute value equation contains the
less than inequality then you will set up
the following expression. Step One
Rewrite the equation with 4X 11 in middle.
-19 lt 4X 11 lt 19 Place the
negative of the number on the left. Place the
less than symbol next. Put 4X 11 in the
middle. Place the less than symbol next. Put the
original number on the right.
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-19 lt 4X 11 lt 19 Step Two Subtract 11
from three positions in expression. -19 lt 4X
11 lt 19 -11 - 11 -11 -30
0 8 Step Three
Rewrite the expression. -30 lt 4X lt 8
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Step Four Divide all three positions by four.
-30 lt 4X lt 8 4 4
4 Solution -7.5 lt X lt 2