Question

How do you solve \[x - (5 - 3x) = 7x + 4\] ?

Answer 1

Hint: We use the BODMAS rule and proceed in the manner of ‘Bracket Open Division Multiplication Addition and Subtraction’ to solve. Solve the given equation i.e. bring all variable values together on one side and all constant values together on the other side. Cancel possible terms and write the equation in simplest form. In the end the equation will give the value of ‘x’ being equal to constant.

Complete step-by-step solution:
We are given the equation \[x - (5 - 3x) = 7x + 4\]
Since the equation has only one variable i.e. x, we will calculate the value of x.
Open the brackets on the left hand side of the equation and multiply the signs outside the bracket to terms inside the bracket.
\[ \Rightarrow x - 5 + 3x = 7x + 4\]
Add terms with same variable on left hand side of the equation
\[ \Rightarrow 4x - 5 = 7x + 4\]
Shift all variable values to the left hand side of the equation and all constant values to the right hand side of the equation.
\[ \Rightarrow 4x - 7x = 4 + 5\]
Calculate the values on both sides of the equation
\[ \Rightarrow - 3x = 9\]
Cancel same factors from both sides of the equation i.e. -3
\[ \Rightarrow x = - 3\]
\[\therefore \]Solution of the equation \[x - (5 - 3x) = 7x + 4\] is \[x = - 3\]

Note:
Many students try to solve the equation by substituting values of ‘x’ one by one, which is wrong as we have only one variable i.e. x and if we substitute its value we will not get the value of any other variable. Keep in mind the same values can be cancelled from both sides of the equation directly or can be brought to one side of the equation and then subtracted. Also, keep in mind when shifting values from one side of the equation to another side of the equation, always change sign from positive to negative and vice-versa.
Alternate method:
We have \[x - (5 - 3x) = 7x + 4\]
Then opening the bracket on Left hand side we get \[x - 5 + 3x = 7x + 4\]
i.e. \[4x - 5 = 7x + 4\]
We can write right hand side of the equation by breaking the variable term
\[4x - 5 = 7x + 4\]becomes \[4x - 5 = 4x + 3x + 4\]
Cancel same terms from both sides of the equation i.e. 4x
The equation becomes \[ - 5 = 3x + 4\]
Shift constant value to right hand side
\[ \Rightarrow 3x = 4 + 5\]
\[ \Rightarrow x = - 3\]
\[\therefore \]Solution of the equation \[x - (5 - 3x) = 7x + 4\] is \[x = - 3\]