Question

Solve the linear equation \[8x-7-3x=6x-2x-3\]

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method or by shifting the terms. Before doing this, we subtract the like terms in LHS and RHS. After that, we group the variable term on one side of the equation and constant terms on the other side.

Complete step-by-step solution:
Given, \[8x - 7 - 3x = 6x - 2x - 3\].
Now subtract the like terms in the LHS,
\[5x - 7 = 6x - 2x - 3\]
Now subtract the like terms in RHS,
\[5x - 7 = 4x - 3\]
We transpose \[ - 7\] which is present in the left-hand side of the equation to the right-hand side of the equation by adding \[7\]on the right-hand side of the equation.
\[5x = 4x - 3 + 7\]
Similarly, we transpose $4x$ to the LHS by subtracting $4x$ on LHS,
\[5x - 4x = - 3 + 7\]
We can see that the variable ‘x’ and the constants are separated, then
\[ \Rightarrow x = 4\]. This is the required result.

Note: We can cross-check whether the obtained solution is correct or not. Substitute the obtained ‘x’ value in the given problem.
\[8x - 7 - 3x = 6x - 2x - 3\]
\[\Rightarrow 8(4) - 7 - 3(4) = 6(4) - 2(4) - 3\]
\[\Rightarrow 32 - 7 - 12 = 24 - 8 - 3\]
\[\Rightarrow 32 - 19 = 24 - 11\]
\[ \Rightarrow 13 = 13\]. That is, LHS is equal to RHS. Hence the obtained answer is correct.
In the above, we did the transpose of addition and subtraction. Similarly, if we have multiplication, we use division to transpose. If we have division, we use multiplication to transpose. Follow the same procedure for these kinds of problems.