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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.


A) x < 5


B) –6x – 5 < 10 – x


C) –6x + 15 < 10 – 5x


D) A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.


E) A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Which are correct representations of the inequality 32x 5 lt 52 x Select two optionsA x lt 5B 6x 5 lt 10 xC 6x 15 lt 10 5xD A number line from negative 3 to 3 i class=

Respuesta :

Answer:

A and D

Step-by-step explanation:

[tex]-3\left(2x-5\right)<5\left(2-x\right)[/tex]

Use the distributive property: Multiply -3 by (2x-5), and 5 by (2-x):

[tex]-6x+15<10-5x[/tex]

Subtract 15 from both sides:

[tex]-6x+15-15<10-5x-15[/tex]

[tex]-6x<-5x-5[/tex]

Subtract -5x from both sides:

[tex]-6x+5x<-5x-5+5x[/tex]

[tex]-x<-5[/tex]

Multiply both sides by -1:

[tex]-x\times-1>-5\times -1[/tex]

[tex]x>5[/tex]

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