Question

How do you solve 2(x-4)=3x-12?

Answer 1

Hint: We have been given an expression in one variable. We will solve it, first by opening the parenthesis. Then we will write the obtained expression in terms of x, by taking the x components on one side of the equality and the constant terms on the other side and solve the resultant expression to get the value of x.

Complete step-by-step solution:
According to the question, we have been given an expression having one variable x, we have solve this expression to find the value of x,
We will be also using the properties of addition and subtraction to solve the expression for x.
Firstly, we will open up the parenthesis in the given expression, we get
\[2(x-4)=3x-12\]
\[\Rightarrow 2x-8=3x-12\]
To solve for x, we will now separate the x terms on side and other constants on the other side,
We have,
\[\Rightarrow 2x-8=3x-12\]
Subtracting 2x on both sides, we get,
\[\Rightarrow (2x-8)-2x=(3x-12)-2x\]
Since, we are subtracting the same entity on both sides of the equality, the equality is not changed.
On the left hand side or LHS of the equality, we have 2x both as positive and negative, so it gets cancelled and on the RHS (or right hand side) of the equality we will subtract \[3x\] by 2x. We get,
\[\Rightarrow 2x-2x-8=3x-2x-12\]
\[\Rightarrow -8=x-12\]
Now, we will add 12 on either side of the equality so that negative 12 on the RHS gets cancelled and we get the expression for x, so we get,
\[\Rightarrow -8+12=x-12+12\]
\[\Rightarrow 4=x\]
As we know, \[a=b\leftrightarrow b=a\]
\[\Rightarrow x=4\]
Therefore, \[x=4\]

Note: While expressing the expression in terms of the variable use the appropriate factors to cancel out the similar terms, fastening the calculation to find the value of the variable. Avoid mistakes by solving the expression step wise.