Respuesta :

Answer:

The correct line is the third one, x must be less than 16.

Step-by-step explanation:

In order to choose the correct line we first need to solve the inequality, since the lines are a representation of the values of "x" that make the inequality valid. We have:

(1/4)*x + 1 < 5

(1/4)*x < 5 -1

(1/4)*x < 4

x < 4/(1/4)

x < 4*(4/1)

x < 16

Therefore the correct line is the third one, x must be less than 16.

The given inequality is reduced to x < 16 that is,  [tex]x \;\epsilon \; (-\infty,16)[/tex] .Therefore, the number line that shows the value of x is given by option C).

Given :

Expression -    [tex]\dfrac{1}{4}x + 1<5[/tex]

The following steps can be used to evaluate the given inequality:

Step 1 - Subtract 1 from both sides in the given inequality.

[tex]\dfrac{1}{4}x + 1-1<5-1[/tex]

[tex]\dfrac{1}{4}x <4[/tex]

Step 2 - Multiply by 4 from both sides in the above expression.

[tex]\dfrac{1}{4}x\times 4 < 4\times 4[/tex]

x < 16

So, the given inequality is reduced to x < 16. Therefore,  [tex]x \;\epsilon \; (-\infty,16)[/tex] .

Therefore, the number line that shows the value of x is given by option C).

For more information, refer to the link given below:

https://brainly.com/question/25140435

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