SOLUTION: i) Sketch on the same diagram the graphs of y = |2x + 3| and {{{y = 1 - x}}}. ii) Find the values of x for which x + |2x + 3| = 1 *Please answer as soon as possible and als

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You can think of as
the same as , except that
whenever is negative, you just ignore the
minus sign and make positive.
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Note that when , since



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When , then
becomes negative, but you just ignore the minus sign.
Graphically, that amounts to reflecting the line
about the y-axis so that ends up positive
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Here's the graph so far:

and, adding ,

Now I want all for which
Now subtract from both sides

This is just the solutions, or intersections of the graphs.
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The reflected part of will have slope =
and the y-intercept is so the equation is
So I want the solutions to:
(1)
(2)
(3)
(3) and (1):



and



(-2/3, 5/3) is a solution
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(3) and (2):


and



(-4, 5) is a solution
The answer to (II) is
and