Question

Resolva as seguintes equações modulares:
a) |x – 5| = 3
b) |3x – 1| = – 5
c) |2x – 1| = x + 3
d) |3x – 5| = |x + 3|

por favorrrrrr

Answer 1

Explicação passo-a-passo:

a)

$|x - 5| = 3$

$x = 8 \\ x = 2$

$\red{x_{1} = 2} \\ \red{x_{2} = 8}$

b)

$|3x - 1| = - 5$

$\red{x∈Ø}$

c)

$|2x - 1| = x + 3$

$|2x - 1| - x =3$

$2x - 1 - x = 3 \\ - (2x - 1) - x = 3$

$x = 4 \\ x = - \frac{2}{3}$

$x = 4 \\ x = - \frac{2}{3}$

$\red{ x_{1} = - \frac{2}{3} } \\ \red{x = 4}$

d)

$|3x - 5| = |x + 3|$

$3x - 5 = x + 3 \\ 3x - 5 = - (x + 3)$

$x = 4 \\ x = \frac{1}{2}$

$\red{x_{1} = \frac{1}{2}} \\\red{ x = 4}$