Question

How do you solve \[2x + 4 = 4x - 2\] ?

Answer 1

Hint: We are asked to solve the given expression \[2x + 4 = 4x - 2\]. The variable in the expression is \[x\] so we will need to solve for \[x\]. The variable \[x\] is on both sides of the equation, so you need to bring \[x\] on one side of the equation. For this use subtraction or addition.

Complete step by step solution:
Given, the expression \[2x + 4 = 4x - 2\]. We are asked to solve this expression, that is we need to find the value of \[x\]. We observe that there is \[x\] on both sides that is on L.H.S and R.H.S. So, we will bring \[x\] on one side to find the value of \[x\]. Let us bring\[x\] on L.H.S. To bring \[x\] on L.H.S we subtract \[ - 4x\] from both L.H.S and R.H.S so that the term \[4x\] on R.H.S vanishes.
Therefore,
\[2x + 4 - 4x = 4x - 2 - 4x\]
\[ \Rightarrow \left( {2x - 4x} \right) + 4 = \left( {4x - 4x} \right) - 2\]
\[ \Rightarrow - 2x + 4 = - 2\] (i)
Now, to keep just \[x\] on L.H.S we subtract \[ - 4\] from both sides of equation (i)
\[ - 2x + 4 - 4 = - 2 - 4\]
\[ \Rightarrow - 2x = - 6\]
Now we multiply by \[ - 1\] on both sides and we get,
\[\left( { - 1} \right) - 2x = \left( { - 1} \right) - 6\]
\[ \Rightarrow 2x = 6\]
Diving by \[2\] on both sides we get,
\[\dfrac{{2x}}{2} = \dfrac{6}{2}\]
\[ \therefore x = 3\]

Therefore, solving \[2x + 4 = 4x - 2\] we get, \[x = 3\].

Note: Whenever we are given to solve a given expression or equation, check the variable in the expression and find the value of that variable. To get the value of a variable you will need to bring the variable on one side of the equation, for this try to eliminate other constants from that side of the equation. Also, remember whenever you add, subtract, multiply or divide on one side of the equation, you will need to do the same on the other side too.