Does 3(7x +7) + 5x represent a number that is greater than, less than, or equal to 5(5x + 10)

Step-by-step explanation:

from

3(7x +7) + 5x = 5(5x + 10)

21x+21+5x     = 25x + 50

26x + 21        = 25x + 50

26x-25x +21 = 50

1x+21            = 50

1x                 =50-21

            x      = 29

equal when x= 29

try to x> 29      such as 30  

3(7(30) +7) + 5(30)     ?    5(5(30) + 10)

1470    ?      800

so  greater than when x >29

finally  

less than when x<29

When x = 29:   the expressions are equal

When x < 29:   3(7x + 7) + 5x is less than 5(5x + 10)

When x > 29:    3(7x + 7) + 5x is greater than 5(5x + 10)

Step-by-step explanation:

Given expressions:

Expand both expressions:

   3(7x + 7) + 5x

⇒ 21x + 21 + 5x

⇒ 26x + 21

   5(5x + 10)

⇒ 25x + 50

Equate the expanded expressions and solve for x

   26x + 21 = 25x + 50

⇒ 26x - 25x = 50 - 21

⇒ x = 29

Therefore, the expressions are equal when x = 29

When x < 29:    3(7x + 7) + 5x < 5(5x + 10)

When x > 29:    3(7x + 7) + 5x > 5(5x + 10)