Răspuns :
Explicație pas cu pas:
[tex] \large \bf a) \: \: -4-{6-[-3+(-3)+(-5-x)-7]-9}=1[/tex]
[tex]\large \bf -{6-[-3+(-3)+(-5-x)-7]-9}=1 + 4[/tex]
[tex]\large \bf -6 + [-3+(-3)+(-5-x)-7] + 9=5[/tex]
[tex]\large \bf [-3+(-3)+(-5-x)-7]=5 + 6 - 9[/tex]
[tex]\large \bf -3+(-3)+(-5-x)-7=2[/tex]
[tex]\large \bf -3-3+(-5-x)-7=2[/tex]
[tex]\large \bf -6+(-5-x)-7=2[/tex]
[tex]\large \bf (-5-x)=2 + 6 + 7[/tex]
[tex]\large \bf -5-x=15[/tex]
[tex]\large \bf -x=15 + 5[/tex]
[tex]\large \bf -x=20[/tex]
[tex] \color{red}\Large \boxed{\bf x= - 20\in\mathbb{Z} }[/tex]
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[tex] \large \bf b)\:\: 5(1-2x)+1=4(x+3)+8[/tex]
[tex] \large \bf 5-10x+1=4x+12+8[/tex]
[tex]\large \bf 6-10x=4x+20[/tex]
[tex]\large \bf 6=4x+20 + 10x[/tex]
[tex]\large \bf 6 - 20=14x[/tex]
[tex]\large \bf - 14=14x \: \: \: \: \bigg|: 14[/tex]
[tex] \color{blue}\Large \boxed {\bf x=- 1\in\mathbb{Z}}[/tex]
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[tex] \large \bf c) \:\: |2x-3|=11[/tex]
[tex]\large \bf 2x-3=11 \implies2x = 14 \implies \boxed{ \bf x_{1} = 7}[/tex]
[tex]\large \bf 2x-3= - 11 \implies2x = - 8 \implies \boxed{ \bf x_{2} = - 4}[/tex]
[tex] \color{limegreen}\Large \bf \implies \boxed{ \bf x \in \{ - 4, \: 7\}\in\mathbb{Z}}[/tex]
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[tex] \large \bf d) \:\: 5( - 3+x)= - (4 - x)+( - 3 \cdot7+2x)[/tex]
[tex] \large \bf - 15+x= -4 + x+( - 21+2x)[/tex]
[tex]\large \bf - 15+x= -4 + x - 21+2x[/tex]
[tex]\large \bf - 15+x= - 25+3x[/tex]
[tex]\large \bf - 15= - 25+3x - x[/tex]
[tex]\large \bf - 15 + 25= 2x[/tex]
[tex]\large \bf 10= 2x[/tex]
[tex] \color{blueviolet}\Large \boxed{\bf x=5\in\mathbb{Z}}[/tex]
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[tex] \large \bf e)\:\: |3y+4 1| =26[/tex]
[tex] \large \bf 3y+41 =26 \implies3y = - 15 \implies \boxed{ \bf y_{1} = - 5 \in \mathbb{Z}}[/tex]
[tex] \large \bf 3y+4=- 26 \implies3y =- 67\implies \boxed{ \bf y_{2}=- \dfrac{67}{3} \not\in \mathbb{Z}}[/tex]
[tex] \color{orangered} \Large \implies \boxed{ \bf y = - 5 \in \mathbb{Z}}[/tex]
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[tex] \large \bf f) \: z(z-4)=z(z+4)-(-24)[/tex]
[tex]\large \bf z^{2}-4z=z^{2} +4z + 24[/tex]
[tex]\large \bf -4z=4z + 24[/tex]
[tex]\large \bf -4z - 4z = 24[/tex]
[tex]\large \bf -8z= 24 \: \: \: \bigg|: ( - 8)[/tex]
[tex] \color{purple}\Large \boxed{\bf z= - 3 \in \mathbb{Z}}[/tex]
P.S.: Dacă ești pe telefon glisează spre stânga pentru a vedea întreaga rezolvare.
Baftă multă!
#copaceibrainly
