Which sentence can represent the inequality One-half x + three-fourths greater-than-or-equal-to 5 and one-fourth?
The sum of half of a number and three-fourths is at least five and one quarter.
Half the sum of a number and three-fourths is not more than five and one quarter.
The sum of half of a number and three-fourths is at most five and one quarter.
Half the sum of a number and three-fourths is not less than five and one quarter.

  The sum of half of a number and three-fourths is at least five and one quarter

Step-by-step explanation:

It's all about making sense of an English sentence.

  "half the sum ..." is different from "the sum of half ..."

And ...

  "at least" and "not less than" mean the same (≥)

  "not more than" and "at most" mean the same (≤)

Since all of the expressions are written out in words, it is a matter of matching the ideas expressed. That's a problem in reading comprehension, not math.

__

"One-half x + three-fourths [is] greater-than-or-equal-to 5 and one-fourth"

  means the same as ...

"The sum of half of a number and three-fourths is at least five and one quarter"

i would pic false cause it goes down towards negative

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is