College Algebra, Chapter 1, 1.1, Section 1.1, Problem 82

Determine the solution of the equation $\displaystyle \frac{1.73 x}{2.12+x} = 1.51$ correct to two decimals

$\begin{equation} \begin{aligned} \frac{1.73 x}{2.12+x} &= 1.51 && \text{Multiply both sides by } (2.12 +x)\\ \\ \cancel{(2.12+x)} & \left[ \frac{1.73x}{\cancel{2.12+x}} = 1.51 \right] (2.12+x) && \text{Cancel out like terms}\\ \\ 1.73 x &= 1.51(2.12+x) && \text{Apply Distributive Property}\\ \\ 1.73 x &= 3.2012 + 1.51 x && \text{Combine like terms}\\ \\ 1.73x - 1.51x &= 3.2012 + 1.51 x - 1.51 x && \text{Simplify}\\ \\ 0.22x &= 3.2012 && \text{Divide both sides by 0.22}\\ \\ \frac{\cancel{0.22}x}{\cancel{0.22}} &= \frac{3.2012}{0.22} && \text{Simplify}\\ \\ x &= 14.55 \end{aligned} \end{equation}$