Question

If $$\dfrac{t+5}{t-5} =10$$, what is the value of t?
A. $$\dfrac{45}{11}$$
B. 5
C. $$\dfrac{11}{2}$$
D. $$\dfrac{55}{9}$$

Answer 1

Hint: In this question it is given that we have to solve $$\dfrac{t+5}{t-5} =10$$.
So to find the solution we need to first make the denominator of LHS as 1 by multiplying some value on the both side of the equation and after that by using addition or subtraction we are going isolate the variable term on one side of the equation and after by division we will get the value of t.

Complete step-by-step answer:
Given equation,
$$\dfrac{t+5}{t-5} =10$$
Since the denominator of the LHS is there so first of all we are going to multiply (t-5) on the both side of the equation,
$$\dfrac{\left( t+5\right) }{\left( t-5\right) } \times \left( t-5\right) =10\times \left( t-5\right) $$
In the left side (t-5) term will got cancelled,
$$t+5=10\times \left( t-5\right) $$
Now on the right side of the equation we are going to remove the parentheses by using distributive property, i.e 10 will multiply with each an every under bracket term.
Therefore from the above equation we get,
$$t+5=10\times t-10\times 5$$
$$\Rightarrow t+5=10t-50$$
Now we can write the above equation as,
$$10t-50=t+5$$
Now we are going to ad 50 on the both side of the equation,
i.e, $$10t-50+50=t+5+50$$
$$\Rightarrow 10t=t+55$$
Now again in order to take like term in one side of the equation, we are going to subtract ‘t’ on from the both side, we get,
$$ 10t-t=t+55-t$$
$$\Rightarrow 9t=55+t-t$$
$$\Rightarrow 9t=55$$
Now to get the value of t we have to divide both sides of the equation by the coefficient of t which is 9.
$$\therefore \dfrac{9t}{9} =\dfrac{55}{9}$$
$$\Rightarrow t=\dfrac{55}{9}$$
Therefore the value of t is $$\dfrac{55}{9}$$.
Hence the correct option is option D.

Note: While solving a linear equation in one variable the following steps provide a good method to use.
Firstly, simplify each side of the equation by removing parentheses and combining like terms.
Secondly, use addition or subtraction to isolate the variable term on one side of the equation.
Thirdly, use multiplication or division to solve for the variable.
Also you need to know that fractions may be removed by multiplying each side of the equation by the common denominator.