Question

Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38?

a) number line with an open dot at 2 with shading to the left and another open dot at 8 with shading to the right

b) number line with an open dot at 8 and at 2 with shading in between

c) number line with a closed dot on 2 and an open dot on 8 and shading in between

d) number line with closed dots at 2 and 8 with shading between the 2 and the 8

Answer 1

we can translate the given statement into-8 ≥ -5x + 2 > -38. 
In this case, we can dissect the inequality into two parts: 
-8 ≥ -5x + 2  and -5x + 2 > -38 

-8 ≥ -5x + 2 5x ≥ 10x ≥ 2 (closed dot)
-5x + 2 > -38 5x < 40x < 8 (open dot)
The answer then is c) number line with a closed dot on 2 and an open dot on 8 and shading in between

Answer 2

c). number line with a closed dot on 2 and an open dot on 8 and shading in between.

Further explanation

Question:

Find out the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38.

Problem-solving:

From the sentence above, we write in mathematical inequality as follows.

$\boxed{ \ -8 \geq -5x + 2 > -38 \ }$

All sides are subtracted by two.

$\boxed{ \ -8 - 2 \geq -5x + 2 - 2 > -38 - 2 \ }$

$\boxed{ \ -10 \geq -5x > -40 \ }$

All sides are divided by -5.

$\boxed{ \ \frac{-10}{-5} \geq \frac{5x}{-5} > \frac{-40}{-5} \ }$

If both (all) sides of an inequality are multiplied or divided by a negative number, the direction of the resulting inequality must be reserved, or in other words, the order of the inequality is reserved.

Thus, the results are as follows:

• $\boxed{\boxed{ \ 2 \leq x < 8 \ }}$, or
• the interval notation is $\boxed{\boxed{ \ [2, 8) \ }}$

The correct graph is number line with a closed dot on 2 and an open dot on 8 and shading in between.

Learn more

1. How many solutions exist for the given equation?  https://brainly.com/question/11306893#
2. Solving a system of linear equations in two variables https://brainly.com/question/11549940#
3. Three multiple-choice questions https://brainly.com/question/1979240  

Keywords: which of the following, the correct graph, the solution to the inequality, −8 greater than or equal to, −5x + 2 > −38, subtracted by, divided by, the interval notation