Question

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

Answer 1

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

Answer 2

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)

Explanation:

Given expressions:

• 3(7x + 7) + 5x
• 5(5x + 10)

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)