Question

Solve $3(x + 2) - 2(x - 1) = 7$ for the value of x.

Answer 1

Hint: First of all take the given expression, open the bracket in the equation multiplying the term outside the bracket inside the bracket and then move all the terms on one side of the equation, then will find the resultant required value for “x”.

Complete step by step solution:
Take the given expression: $3(x + 2) - 2(x - 1) = 7$
Open the bracket multiplying the term outside with the terms inside the bracket. When there is a negative sign outside the bracket then the sign of the terms inside the bracket changes when opened and there is no change in the terms when there is a positive sign outside the bracket.
$ \Rightarrow 3x + 6 - 2x + 1 = 7$
Move all the terms on the left hand side of the equation, when you move any term from one side to another then the sign of the terms also changes. Positive term becomes negative term.
$ \Rightarrow 3x + 6 - 2x + 1 - 7 = 0$
Take like terms together, like terms are the terms with the same variable and its power.
$ \Rightarrow \underline {3x - 2x} + \underline {6 + 1 - 7} = 0$
combine the like terms, when you add one positive term and one negative term you have to do subtraction and give sign of the bigger number to the resultant value.
$ \Rightarrow x + 0 = 0$
Above expression can be re-written as –
$ \Rightarrow x = 0$
This is the required solution.

Thus the required solution is x = 0.

Note: Be very careful while simplification of the terms. When you open the brackets and there is a negative sign outside the bracket then the sign of the terms inside the bracket will be changed. Positive terms will become negative and negative terms become positive. Also, remember when there is a positive sign outside the bracket then the sign of the terms inside the bracket do not change and remains the same.