6. which inequality represents the solution
to 1.25x + 2.5 < 2.75x – 6.5?
a)x> 6 b)x> 2.25 c)x< 6
d)x < 2.25

A)    x > 6 is the SOLUTION of the given inequality.

Step-by-step explanation:

Here, the given inequality is given as:

1.25 x + 2.5 <  2.75 x – 6.5

Now, solving the given inequality for the value of x, we get:

1.25 x + 2.5 <  2.75 x – 6.5

Add ( -1 .25 x ) on both sides, we get:

1.25 x + 2.5  + ( -1 .25 x) <  2.75 x – 6.5 + ( -1 .25 x)

⇒ 2.5 <  1. 5 x - 6.5

Add ( 6.5 ) on both sides, we get:

2.5  + (6.5) < 1. 5 x - 6.5 + (6.5)

or,  9.0 < 1.5 x

Divide by  (1.5 ) on both sides, we get:

6 <  x

or, x > 6

Hence, x > 6 is the SOLUTION of the given inequality.

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