Jamya Elliott

2022-01-23

Determine the solution ${S}_{x}$ of the equation and inequalities over Z.
1) $|4x+5|=11$
2) $|7x+6|=25$
3) $|2x-11|=20$
4) $|3x-1|=-2$
5) $|2x+3|<8$

Tapanuiwp

Expert

1) $|4x+5|=11$

$⇒4x=11-5=6$
$⇒x=\frac{6}{4}=\frac{3}{2}$

$⇒4x+5=-11$
$⇒4x=-16$
$⇒x=-4$
$\therefore |4x+5|=11$
$⇒{S}_{x}=\left[-4\right]$
2) $|7x+6|=25$

$⇒7x=25-6=19$
$⇒x=\frac{19}{7}$

$⇒7x+6=-25$
$⇒7x=-31$
$⇒x=-\frac{31}{7}$
There doesn't exist any solution over Z

lirwerwammete9t

Expert

3. $|2x-11|=20$

$⇒2x=31$
$⇒x=\frac{31}{2}$

$⇒2x-11=-20$
$⇒2x=-9$
$⇒x=-\frac{9}{2}$
There isnt

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