Question

How do you solve $\dfrac{3}{5}d+5=\dfrac{1}{3}d-3$ ?

Answer 1

Hint: First of all we will combine the equal like terms one side of the equal sign and by placing numbers on the other side of the equal sign. Then, we will use the properties of addition and the properties of multiplication for solving the given question that is $\dfrac{3}{5}d+5=\dfrac{1}{3}d-3$ .

Complete step-by-step answer:
Since, the given question is:
$\Rightarrow \dfrac{3}{5}d+5=\dfrac{1}{3}d-3$
As we can see that $\dfrac{3}{5}d$ and $\dfrac{1}{3}d$ are equal terms. So, we will combine them by placing one side of the equal sign and will do the same with numbers by placing them on the other side of the equal sign. Since, we will change the place; the sign of the term that changed its place will be change as:
$\Rightarrow \dfrac{3}{5}d-\dfrac{1}{3}d=-3-5$
Here, we will multiply by $15$ both sides of the above step to remove denominator as:
$\Rightarrow 15\times \dfrac{3}{5}d-15\times \dfrac{1}{3}d=15\times \left( -3-5 \right)$
After solving above step, we will have:
$\Rightarrow 3\times 3d-5\times 1d=15\times \left( -3-5 \right)$
Now, we will complete the multiplication both side of the above step as:
$\Rightarrow 9d-5d=-45-75$
Now, we will use subtraction for equal like terms and will add numbers of other side of equal sign because it has same signs as:
$\Rightarrow 4d=-120$
Here, we will divide by $4$ both sides in the above step as:
$\Rightarrow \dfrac{4d}{4}=\dfrac{-120}{4}$
Here, we will have after division by $4$ as:
$\Rightarrow d=-30$
Hence, after solving the given question that is $\dfrac{3}{5}d+5=\dfrac{1}{3}d-3$ , we got the value as $d=-30$ .

Note: Here, we can check if the solution is correct or not in the following way as:
Since, we obtained from the solution:
$\Rightarrow d=-30$
Now, we will apply this value in the given question that is:
$\Rightarrow \dfrac{3}{5}d+5=\dfrac{1}{3}d-3$
Since, we already got the value of the $d$ , we will use it in the question below as:
$\Rightarrow \dfrac{3}{5}\times -30+5=\dfrac{1}{3}\times -30-3$
Now, we will do division then multiplication as:
$\Rightarrow 3\times -6+5=1\times -10-3$
Here, after multiplication, we will have:
$\Rightarrow -18+5=-10-3$
Then, we will do addition and subtraction whatever required as:
$\Rightarrow -13=-13$
Since, $L.H.S.=R.H.S.$
Hence, the solution is correct.