How many solutions exist for the given equation? 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)?
Zero, One, Two, Infinitely many

Solution:

Given: 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)

Using the distributive property of multiplication

0.75x + 30 = 0.35x + 7 + 0.35x + 7

By grouping the like terms

0.75x + 30 = 0.7x + 14

0.75x - 0.7x = 14 - 30

So we get,

0.05x = -16

Divide both sides by 0.05

x = - 16/0.05

= -320

Therefore, one solution exists.

How many solutions exist for the given equation? 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)?

Summary:

One solution exists for the given equation 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20).