Question

How do you solve and check \[ - 6x - 7 = - 1( - 9 + 2x)\] ?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity).

Complete step-by-step answer:
Given, \[ - 6x - 7 = - 1( - 9 + 2x)\] .
Expanding the brackets in the right hand side of the equation,
 \[ \Rightarrow - 6x - 7 = 9 - 2x\]
We transpose \[ - 2x\] on the left hand side of the equation by adding \[2x\] on the left hand side. Similarly we transpose \[ - 7\] on the right hand side of the equation by adding 7 to the left hand side of the equation.
 \[ - 6x + 2x = 9 + 7\]
Taking ‘x’ common in left hand side of the equation,
 \[x( - 6 + 2) = 9 + 7\]
 \[ - 4x = 16\]
Dividing by \[ - 4\] on both side we have
 \[x = - \dfrac{{16}}{4}\]
 \[ \Rightarrow x = - 4\] . This is the required answer.
To check the answer all we need to do is substituting the ‘x’ value in the given problem we have,
 \[ - 6x - 7 = - 1( - 9 + 2x)\]
 \[\left( { - 6 \times - 4} \right) - 7 = - 1( - 9 + \left( {2 \times - 4} \right))\]
 \[24 - 7 = - 1( - 9 - 8)\]
 \[17 = - 1( - 17)\]
 \[ \Rightarrow 17 = 17\] . Hence the obtained answer is correct.
So, the correct answer is “ x = - 4”.

Note: In the right hand side of the equation we expand the brackets. We know that the product of negative numbers with negative numbers will have positive numbers. Also product of positive number with negative number we will get negative number. If we want to transpose the addition number to any side of the equation we subtract it with the same number on both sides of the equation. Similarly if we want to transpose the negative number to any side of the equation we add with the same number on both sides of the equation. 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.