Question

Find the value of x for the provided equation 0.09(x+200)=0.08x+22.

Decimals
Find the value of x for the provided equation $$\displaystyle{0.09}{\left({x}+{200}\right)}={0.08}{x}+{22}.$$

Procedure: To solve the equation that involve decimals, there are two commonly used procedures. One procedure is to keep the numbers in decimal form, then solve the equation by applying the properties. Second procedure is to multiply both sides of the equation by an appropriate power of 10 to clear the equation of all decimals. Calculation: Consider, $$\displaystyle{0.09}{\left({x}+{200}\right)}={0.08}{x}+{22}$$ Since, clear the decimals by multiplying both sides of the equation by 100. $$\displaystyle{100}{\left[{0.09}{\left({x}+{200}\right)}\right]}={100}{\left[{0.08}{x}+{22}\right]}$$
$$\displaystyle{9}{\left({x}+{200}\right)}={100}{\left({0.08}{x}+{22}\right)}$$
$$\displaystyle{9}{x}+{1800}={9}{x}+{2200}$$, apply distributive property on the both side. $$\displaystyle{9}{x}-{8}{x}={2200}-{1800}$$
$$\displaystyle{x}={400}$$ Thus, the solution is $$\displaystyle{x}={400}.$$ Answer: The solution set is x=400.