Question

How do you solve $12=-3\left( 2x+1 \right)+7x$?

Answer 1

Hint: Now to solve the given equation we will first open the brackets in the equation with the help of distributive property. Now we will separate the variables and the constants in the equation. Now simplify the equation to find the required value of x.

Complete step by step solution:
Now consider the given equation $12=-3\left( 2x+1 \right)+7x$
Now the equation given is a linear equation in one variable. To find the solution of the equation we will try to write it in the form $ax=b$ .
Let us first simplify the given equation by opening the bracket.
By distributive property we know that $a\left( b+c \right)=ab-ac$ . Hence using this in the equation we get,
$\Rightarrow 12=-6x-3+7x$
Now we will separate the variables and the constants in the above equation. To do so we will transpose 3 from RHS to LHS. Hence we get,
$\Rightarrow 12+3=7x-6x$
Now we know that we can 7x – 6x = x. Hence using this in the above equation we get,
$\Rightarrow x=15$
Hence we get the value of x = 15.
Hence the solution of the given equation is x = 15.

Note:
Now note that while transposing the terms from LHS to RHS the sign of the term changes. Hence if we transpose positive term it will become negative and if we transpose negative term it will become positive. Hence in the above example when we transpose 3 it becomes positive. Now also note that if the coefficient of x is not 1 after simplifying we shall make it 1 by dividing the whole equation by coefficient of x.