how many solutions exist for the given equation?\n0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20)\nzero\none\ntwo\…

Explanation:

Step1: Simplify the right - hand side

First, simplify (0.35(x + 20)+0.35(x + 20)). Using the distributive property (a(b + c)=ab+ac), we have (0.35(x + 20)+0.35(x + 20)=(0.35 + 0.35)(x + 20)=0.7(x + 20)). The equation becomes (0.75(x + 40)=0.7(x + 20)).

Step2: Expand both sides

Expand (0.75(x + 40)) using the distributive property: (0.75x+0.75\times40 = 0.75x + 30). Expand (0.7(x + 20)) using the distributive property: (0.7x+0.7\times20=0.7x + 14). The equation is now (0.75x+30 = 0.7x + 14).

Step3: Move the (x) terms to one side and constants to the other side

Subtract (0.7x) from both sides: (0.75x-0.7x+30=0.7x - 0.7x+14), which gives (0.05x+30 = 14). Subtract 30 from both sides: (0.05x+30 - 30=14 - 30), so (0.05x=-16).

Step4: Solve for (x)

Divide both sides by (0.05): (x=\frac{-16}{0.05}=-320).

Answer:

one