Question

Find the value of x, \[\dfrac{4x}{7}-12=7\] (write answer up to 1 decimal point).

Answer 1

Hint: Our given equation is \[\dfrac{4x}{7}-12=7\] . Now, shift the constant number 12 to the RHS of the equation \[\dfrac{4x}{7}-12=7\] . Then, divide the equation by 4, we will get \[\dfrac{1}{4}.\dfrac{4x}{7}=\dfrac{12+7}{4}\] . After this, multiply the LHS and RHS of the equation \[\dfrac{1}{4}.\dfrac{4x}{7}=\dfrac{12+7}{4}\] by 7 and solve it further.

Complete step-by-step answer:

According to the question, it is given that our equation is \[\dfrac{4x}{7}-12=7\] ………………(1)
We can see that equation (1) is a linear equation in x. Here, we have to solve equation (1) and get the value of x.
In equation (1), shifting the constant number 12 to the RHS, we get
\[\begin{align}
  & \dfrac{4x}{7}-12=7 \\
 & \Rightarrow \dfrac{4x}{7}=7+12 \\
\end{align}\]
\[\Rightarrow \dfrac{4x}{7}=19\] …………………..(2)
We have to further simplify the linear equation in equation (2).
Dividing equation (2) by 4, we get
\[\Rightarrow \dfrac{1}{4}\times \dfrac{4x}{7}=19\times \dfrac{1}{4}\]
\[\Rightarrow \dfrac{x}{7}=\dfrac{19}{4}\] ………………(3)
Now, multiplying equation (3) by 7, we get
\[\Rightarrow 7.\dfrac{x}{7}=7.\dfrac{19}{4}\]
\[\Rightarrow x=\dfrac{133}{4}=33.25\]
We have to answer up to one decimal point, that is we have to round the number 33.25 up to one decimal point.
We have to circle the number with one decimal place (up to and including the first digit after the decimal point)
Now, circle the number (33.2)5.
Looking at the next digit after the circled number, we have the next digit equal to 5.
We know the rule to round off a number,
 If the next digit is 0, 1, 2, 3, or 4, then our circled number is the answer.
 If the next digit is 5, 6, 7, 8, or 9, then add 1 to the last digit of our circled number.
Here, we have the next digit equal to 5, so (33.2) + .1 = 33.3
Hence, the value of x is 33.3.

Note: In this question, one can make a mistake in shifting -12 of LHS to the RHS and write -12 in RHS too, which is wrong. If we are moving some terms of LHS to RHS then its sign is changed and vice-versa. Here we are moving -12 to the RHS. So, we have to write +12 in the RHS of the equation. At the time while rounding off we have to be careful. One can round off the number 33.25 as 33.2 which is wrong. We have to round off up to one decimal point. Here the next digit is 5. So, we have to add 1 to the last digit of our number. So, after rounding off, our number is 33.3.