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−2∣x+4∣=3−4x-2 equation

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Numerical solution:

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The solution

You have entered [src]
-2*|x + 4| = 3 - 4*x - 2
$$- 2 \left|{x + 4}\right| = \left(3 - 4 x\right) - 2$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
$$x + 4 \geq 0$$
or
$$-4 \leq x \wedge x < \infty$$
we get the equation
$$4 x - 2 \left(x + 4\right) - 1 = 0$$
after simplifying we get
$$2 x - 9 = 0$$
the solution in this interval:
$$x_{1} = \frac{9}{2}$$

2.
$$x + 4 < 0$$
or
$$-\infty < x \wedge x < -4$$
we get the equation
$$4 x - 2 \left(- x - 4\right) - 1 = 0$$
after simplifying we get
$$6 x + 7 = 0$$
the solution in this interval:
$$x_{2} = - \frac{7}{6}$$
but x2 not in the inequality interval


The final answer:
$$x_{1} = \frac{9}{2}$$
The graph
Sum and product of roots [src]
sum
9/2
$$\frac{9}{2}$$
=
9/2
$$\frac{9}{2}$$
product
9/2
$$\frac{9}{2}$$
=
9/2
$$\frac{9}{2}$$
9/2
Rapid solution [src]
x1 = 9/2
$$x_{1} = \frac{9}{2}$$
x1 = 9/2
Numerical answer [src]
x1 = 4.5
x1 = 4.5