Question

Ecuaciones de desigualación....
a) -7<4x+1<13
b) -6<2x-3<4
c) -8≤3x+1≤-2

Answer 1

Ecuaciones de des igualación.

a) -7<4x+1<13

$-7\ \textless \ 4x+1\ \textless \ 13$
$\left(-7\ \textless \ 4x+1\right)\quad \mathrm{and}\quad \left(4x+1\ \textless \ 13\right)$
$-7\ \textless \ 4x+1$
$4x+1\ \textgreater \ -7$
$4x+1-1\ \textgreater \ -7-1$
$4x\ \textgreater \ -8$
$x\ \textgreater \ -2$
$4x+1\ \textless \ 13$
$4x\ \textless \ 12$
$x\ \textless \ 3$
$\mathrm{Combinar\:los\:rangos}$
$-2\ \textless \ x\ \textless \ 3$
$-7\ \textless \ 4x+1\ \textless \ 13\quad :\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-2\ \textless \ x\ \textless \ 3\:\\ \:\mathrm{Notacion\:intervalo}&\:\left(-2,\:3\right)\end{bmatrix}$

b) -6<2x-3<4

$\left(-6\ \textless \ 2x-3\right)\quad \mathrm{and}\quad \left(2x-3\ \textless \ 4\right)$
$-6\ \textless \ 2x-3$
$2x-3\ \textgreater \ -6$
$2x\ \textgreater \ -3$
$x\ \textgreater \ -\frac{3}{2}$

$2x-3\ \textless \ 4$
$2x\ \textless \ 7$
$x\ \textless \ \frac{7}{2}$
$\mathrm{Combinar\:los\:rangos}$
$-\frac{3}{2}\ \textless \ x\ \textless \ \frac{7}{2}$
$-6\ \textless \ 2x-3\ \textless \ 4\quad :\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-\frac{3}{2}\ \textless \ x\ \textless \ \frac{7}{2}\:\\ \:\mathrm{Decimal:}&\:-1.5\ \textless \ x\ \textless \ 3.5\\ \mathrm{Notacion\:intervalo}&\:\left(-\frac{3}{2},\:\frac{7}{2}\right)\end{bmatrix}$

c) -8≤3x+1≤-2

$\left(-8\le \:3x+1\right)\quad \mathrm{and}\quad \left(3x+1\le \:-2\right)$
$-8\le \:3x+1$
$3x\ge \:-9$
$x\ge \:-3$

$3x+1\le \:-2$
$3x\le \:-3$
$x\le \:-1$
$\mathrm{Combinar\:los\:rangos}$
$-3\le \:x\le \:-1$
$-8\le \:3x+1\le \:-2\quad :\quad \begin{bmatrix}\mathrm{Solucion:}\:&\:-3\le \:x\le \:-1\:\\ \:\mathrm{Notacion\:intervalo}&\:\left[-3,\:-1\right]\end{bmatrix}$