Question

1. Rezolvați în Z următoarele ecuații:

a) -4-{6-[-3+(-3)+(-5-x)-7]-9}=1; b) 5(1-2x)+1=4(x+3)+8; c) |2x-3|=11; d) 5(─3+x)=─(4─x)+(─3∙7+2x);

e)│3y+41│=26; f) z(z─4)=z(z+4)─(─24);​​

Answer 1

Explicație pas cu pas:

$\large \bf a) \: \: -4-{6-[-3+(-3)+(-5-x)-7]-9}=1$

$\large \bf -{6-[-3+(-3)+(-5-x)-7]-9}=1 + 4$

$\large \bf -6 + [-3+(-3)+(-5-x)-7] + 9=5$

$\large \bf [-3+(-3)+(-5-x)-7]=5 + 6 - 9$

$\large \bf -3+(-3)+(-5-x)-7=2$

$\large \bf -3-3+(-5-x)-7=2$

$\large \bf -6+(-5-x)-7=2$

$\large \bf (-5-x)=2 + 6 + 7$

$\large \bf -5-x=15$

$\large \bf -x=15 + 5$

$\large \bf -x=20$

$\color{red}\Large \boxed{\bf x= - 20\in\mathbb{Z} }$

______________________

$\large \bf b)\:\: 5(1-2x)+1=4(x+3)+8$

$\large \bf 5-10x+1=4x+12+8$

$\large \bf 6-10x=4x+20$

$\large \bf 6=4x+20 + 10x$

$\large \bf 6 - 20=14x$

$\large \bf - 14=14x \: \: \: \: \bigg|: 14$

$\color{blue}\Large \boxed {\bf x=- 1\in\mathbb{Z}}$

______________________

$\large \bf c) \:\: |2x-3|=11$

$\large \bf 2x-3=11 \implies2x = 14 \implies \boxed{ \bf x_{1} = 7}$

$\large \bf 2x-3= - 11 \implies2x = - 8 \implies \boxed{ \bf x_{2} = - 4}$

$\color{limegreen}\Large \bf \implies \boxed{ \bf x \in \{ - 4, \: 7\}\in\mathbb{Z}}$

______________________

$\large \bf d) \:\: 5( - 3+x)= - (4 - x)+( - 3 \cdot7+2x)$

$\large \bf - 15+x= -4 + x+( - 21+2x)$

$\large \bf - 15+x= -4 + x - 21+2x$

$\large \bf - 15+x= - 25+3x$

$\large \bf - 15= - 25+3x - x$

$\large \bf - 15 + 25= 2x$

$\large \bf 10= 2x$

$\color{blueviolet}\Large \boxed{\bf x=5\in\mathbb{Z}}$

______________________

$\large \bf e)\:\: |3y+4 1| =26$

$\large \bf 3y+41 =26 \implies3y = - 15 \implies \boxed{ \bf y_{1} = - 5 \in \mathbb{Z}}$

$\large \bf 3y+4=- 26 \implies3y =- 67\implies \boxed{ \bf y_{2}=- \dfrac{67}{3} \not\in \mathbb{Z}}$

$\color{orangered} \Large \implies \boxed{ \bf y = - 5 \in \mathbb{Z}}$

______________________

$\large \bf f) \: z(z-4)=z(z+4)-(-24)$

$\large \bf z^{2}-4z=z^{2} +4z + 24$

$\large \bf -4z=4z + 24$

$\large \bf -4z - 4z = 24$

$\large \bf -8z= 24 \: \: \: \bigg|: ( - 8)$

$\color{purple}\Large \boxed{\bf z= - 3 \in \mathbb{Z}}$

P.S.: Dacă ești pe telefon glisează spre stânga pentru a vedea întreaga rezolvare.

Baftă multă!

#copaceibrainly