Question

How do you solve 2(x-7)-10=12-4x ?

Answer 1

Hint: In this type of question, we will first expand the terms in the parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parentheses. After that, we will rearrange the equation to get into the simplest form. So that we can solve the equation to get the value of x.

Complete step by step answer:
Let us solve the question.
The given equation which we have to solve is
\[2(x-7)-10=12-4x\]
Let us now expand the terms in the parenthesis which is given on the left side of the equation
\[2(x)-2(7)-10=12-4x\]
Now, we will multiply both the terms within the parenthesis by the term outside the parentheses.
\[2x-14-10=12-4x\]
Now, we know that the standard form is x=C, where x is variable and C is constant. We will convert the above equation in the standard form.
We will put all the terms of x in the left side of the equation and all the constant terms in the right side of the equation.
For that we will balance the equation
\[2x-14-10+14+10+4x=12-4x+14+10+4x\]
\[\Rightarrow 2x+6x-14+14-10+10=-4x+4x+12+14+10\]
\[\Rightarrow 6x+0=0+36\]
\[\Rightarrow 6x=36\]
Now, we divide 36 by 6.
\[\Rightarrow x=\dfrac{36}{6}=6\]

So, the correct answer is “6”.

Note: The first degree equations that we consider in this question have at most one solution. The solutions to many such equations can be determined by inspection. We can solve this question using additional subtraction properties.
\[2(x-7)-10=12-4x\]
\[\Rightarrow2x-14-10=12-4x \]
\[\Rightarrow 2x+4x=12+14+10\]
\[\Rightarrow 6x=36\]
Now, we divide 36 by 6 to get the value of x.
\[\Rightarrow x=6.\]
Hence, we are getting the same values using a different method. So, we can also use additional subtraction properties to solve this type of question.