Question

Find the solution of \[180 - x = 10 + 2\left( {90 - x} \right)\].

Answer 1

Hint: Whenever there are questions with brackets, all the brackets should be expanded for calculations. Rearrangement of the equation should be done. Before or after brackets if there is any number then that should be multiplied individually with the numbers which are present inside the bracket. After the expansion the Left Hand Side and the Right Hand Side can be evaluated to find the unknown variable.

Complete answer:
Expanding the brackets we have,
\[180 - x = 10 + 180 - 2x\]
The equation should be distributed by expanding the brackets.
Then we can add 10 and 180 to have,
\[ \Rightarrow 180 - x = 190 - 2x\]
On adding above equation we have,
\[ \Rightarrow 180 = 190 - x\]
Like terms should be combined on one side so that calculations can be done. Since we can only add or subtract the like terms that are variable cannot be added or subtracted with a number.
Subtracting 190 from 180 we have,
\[ \Rightarrow - 10 = - x\]
And then multiplying by -1 gives,
\[ \Rightarrow 10 = x\]
This is the same as \[x = 10\].

Note: If there are questions with brackets then the first step that has to be done is expansion of brackets. If there is any number before a bracket then that number has to be multiplied with each and every number inside the bracket. Any + or – symbol if present then the brackets should be expanded accordingly. During the calculations only like terms can be added or subtracted. So, all the like terms should be taken at one side to find the unknown variable. During changing the sides, the sign must also change.