Question

How do you solve \[8 - 7x = 13x + 8\]?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. That is, we group the ‘y’ terms on one side and constants on the other side of the equation. We can group this by shifting the variables to one side and constant to the other side. We must be careful about the sign changes.

Complete step-by-step solution:
Given, \[8 - 7x = 13x + 8\].
Now we shift the 13x which is present in the R.H.S to the L.H.S. We know that if we shift a positive number from one side of the equation to the other side of the equation the operation addition changes to negative. That is
\[8 - 7x - 13x = 8\]
Similarly we shift the constant 8 from the L.H.S to the R.H.S
\[ - 7x - 13x = 8 - 8\]
We can see that the variable ‘x’ and the constants are separated, then
\[ - 20x = 0\]
Since the right-hand side of the equation is zero, if we divide the whole equation by $-20$ we will have zero as a result.
\[ \Rightarrow x = 0\]. This is the required result.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[8 - 7x = 13x + 8\]
\[8 - 7(0) = 13(0) + 8\]
\[ \Rightarrow 8 = 8\]
Hence the obtained answer is correct.
We should also know the result of the multiplication of two signs. That is the product of two negative numbers results in Positive numbers only. The product of a negative (positive) and a positive (negative) number results in a negative number only.