Respuesta :

mhanifa

Answer:

  • x > 3 or x < - 3

Given equations:

  • −2(x + 4) + 10 < x − 7

or

  • −2x + 9 > 3(x + 8)

Solve each inequality:

  • −2(x + 4) + 10 < x − 7  
  • -2x - 8 + 10 < x - 7
  • -2x - x < -7 - 2
  • -3x < -9
  • 3x > 9
  • x > 3

or

  • −2x + 9 > 3(x + 8)
  • -2x + 9 > 3x + 24
  • -2x - 3x > 24 - 9
  • -5x > 15
  • 5x < -15
  • x < - 3

#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]

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