Question

How many solutions does the following equation have?
$\frac{1}{3}t=-t+\frac{2}{3}t-1$

Answer 1

Detailed step-by-step solution:
Solving equation $\frac{1}{3}t=-t+\frac{2}{3}t-1$ for $t$ to find the number of solutions it could have.
$\frac{1}{3}t=-t+\frac{2}{3}t-1$
$\frac{1}{3}t+t-\frac{2}{3}t=-1$ (transposing $-t+\frac{2}{3}t$ to the left hand side)
$t+3t-2t=-3$ (multiplying the equation with $3$)
$2t=-3$
$t=\frac{-3}{2}$ (dividing both the sides by $2$)
We were able to simplify the original given equation to a form with just the variable on the L.H.S. and a number on the R.H.S. giving $“t”$ a unique value, i.e., $-32.$
As we got only one value of $t;$ therefore, it has only one solution.

So, option A is the correct answer.