Question

How do you solve \[2(3x + 5) = 46\] ?

Answer 1

Hint: We use the BODMAS rule and proceed in the manner of ‘Bracket Open Division Multiplication Addition and Subtraction’ to solve. Cancel common factors from both sides of the equation. 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 \[2(3x + 5) = 46\]
Since the equation has only one variable i.e. x, we will calculate the value of x.
Open the bracket on left hand side of the equation and multiply values outside the bracket to values inside the bracket
\[ \Rightarrow 2 \times 3x + 2 \times 5 = 46\]
Multiply the terms
\[ \Rightarrow 6x + 10 = 46\]
Shift all variable values to the left hand side of the equation and all constant values to right hand side of the equation.
\[ \Rightarrow 6x = 46 - 10\]
Calculate the values on both sides of the equation
\[ \Rightarrow 6x = 36\]
Cancel same factors on both sides of equation i.e. 6
\[ \Rightarrow x = 6\]

\[\therefore \] Solution of the equation \[2(3x + 5) = 46\] is \[x = 6\]

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 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 to solve \[2(3x + 5) = 46\]
We can directly divide both sides by 2
\[ \Rightarrow 3x + 5 = 23\]
Now shift all constants to right hand side
\[ \Rightarrow 3x = 23 - 5\]
\[ \Rightarrow 3x = 18\]
Cancel same factors i.e. 3 from both sides
\[ \Rightarrow x = 6\]
\[\therefore \] Solution of the equation \[2(3x + 5) = 46\] is \[x = 6\]