Question

How do you solve and check your solutions to 7 = $\dfrac{t}{-7}$ ?

Answer 1

Hint: In this problem, we are given a linear equation in one variable. We have to find the variable ‘t’ by solving this equation. We will keep ‘t’ alone on one side in order to solve the like terms. After solving completely, we have to verify the obtained value by placing it in the given equation. If that value satisfies the equation that means the obtained value is correct.

Complete step-by-step answer:
Now, let’s solve the question.
As we know that a linear equation is that equation in which the highest degree of the variable is one. For example: In 3z + 7, ‘z’ has the degree as one. Linear equation in one variable means it contains only a single variable and value needs to be found out. Here, in this question we will find the value of ‘t’ by moving the denominator i.e. -7 on the side. After obtaining the value for ‘t’ we will verify it by placing that obtained value in the given equation. If it satisfies the equation and gives the result as zero that means the obtained value is correct.
Now let’s start.
$\Rightarrow $7 = $\dfrac{t}{-7}$
Take -7 on the other side:
$\Rightarrow 7\times \left( -7 \right)=t$
Solve for t:
$\therefore t=-49$
Now, take the right side of the equation i.e. $\dfrac{t}{-7}$. Replace the obtained value with ‘t’ and check:
 $\Rightarrow \dfrac{t}{-7}\Leftrightarrow \dfrac{-49}{-7}$
After reducing it we will get 7. Which means our answer is verified.

Note: When we take any number or variable to the other side of the equation, then its sign will not change rather the state will change, means just like above, if it is in division on going to another side it will be in product there. Just like this happens in addition and subtraction also. So take care that these types of silly mistakes should not be done.