Question

The given equation is either linear or equivalent to a linear equation. Solve the equation.

$\frac{x}{3}-2=\frac{5}{3}x+7$

Short answer

The solution of linear equation is$x=-\frac{27}{4}$

Step-by-step solution

Step 1. Solving a linear equation.

We solve a linear equation by changing it to an equivalent equation with all terms that have the variable x on one side and all constant terms on the other.

Step 2. Analyze the given expression.

Given

$\frac{x}{3}-2=\frac{5}{3}x+7$

Step 3. Solve.

$\begin{array}{l}\frac{x}{3}-2=\frac{5}{3}x+7\\ \Rightarrow \frac{x}{3}-\frac{5}{3}x=7+\mathrm{2.........}\left[\text{add2andsubtract}\frac{5}{3}x\right]\\ \Rightarrow -\frac{4}{3}x=9\\ \Rightarrow x=-9\cdot \frac{3}{4}\mathrm{...............}\left[\text{multiplyby}\frac{3}{4}\right]\\ \Rightarrow x=-\frac{27}{4}\end{array}$

So, the solution of given equation is$x=-\frac{27}{4}$