Mister Exam
−2∣x+4∣=3−4x-2 equation
The teacher will be very surprised to see your correct solution 😉
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:
$$x_{1} = \frac{9}{2}$$
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:
$$x_{1} = \frac{9}{2}$$
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