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50 PTS AND 25 MORE IF U GET BRAIN PLSSSSSSSSSSSSSSS
Solve the following compound inequality: −2(x + 4) + 10 < x − 7 or −2x + 9 > 3(x + 8)
A: x < 3 or x > −3
B: x > 3 or x < −3
C: x < 7 or x > −3
D: x > 7 or x < −3

Respuesta :

WojtekR

[tex]-2(x+4)+10<x-7 \qquad\vee\qquad -2x+9>3(x+8)\\\\-2\cdot x+(-2)\cdot4+10<x-7 \qquad\vee\qquad -2x+9>3\cdot x+3\cdot8\\\\-2x-8+10<x-7 \qquad\vee\qquad -2x+9>3x+24\\\\-2x-x<-7+8-10 \qquad\vee\qquad -2x-3x>24-9\\\\-3x<-9 \quad|\div(-3)\qquad\vee\qquad -5x>15\quad|\div(-5)\\\\\boxed{x>3\qquad\vee\qquad x<-3}[/tex]

Answer B

#1

[tex]\\ \sf{:}\!\implies -2(x+4)+10<x-7[/tex]

[tex]\\ \sf{:}\!\implies -2x-8+10<x-7[/tex]

[tex]\\ \sf{:}\!\implies x+2x>2+7[/tex]

[tex]\\ \sf{:}\!\implies 3x>9[/tex]

[tex]\\ \sf{:}\!\implies x>\dfrac{9}{3}[/tex]

[tex]\\ \sf{:}\!\implies x>3[/tex]

#2

[tex]\\ \sf{:}\!\implies -2x+9>3(x+8)[/tex]

[tex]\\ \sf{:}\!\implies -2x+9>3x+24[/tex]

[tex]\\ \sf{:}\!\implies -2x-3x>24-9[/tex]

[tex]\\ \sf{:}\!\implies -5x>15[/tex]

[tex]\\ \sf{:}\!\implies x<\dfrac{15}{-5}[/tex]

[tex]\\ \sf{:}\!\implies x<-3[/tex]

Option B

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