Question

How do you solve \[3\left( 2x+4 \right)=2+6x+10\] ?

Answer 1

Hint: We can solve the equation using linear equation concept. First we have to remove the parenthesis and then we have to group the like terms. All the terms containing x on one side and the other terms on the other side. After grouping the terms, we have to further simplify the equation to find the value of x.

Complete step by step solution:
Given equation is
\[3\left( 2x+4 \right)=2+6x+10\]
First we have to simplify the equation by adding the like terms.
After adding we will get
\[\Rightarrow 3\left( 2x+4 \right)=6x+12\]
Now we have to remove the parentheses.
To remove the parentheses we will divide the equation with 3 on both sides.
By dividing the equation with 3 on both sides of the equation we will get
 \[\Rightarrow \dfrac{3\left( 2x+4 \right)}{3}=\dfrac{6x+12}{3}\]
By simplifying we will get
\[\Rightarrow 2x+4=2x+4\]
Now we have group the like terms .
To group like terms we will subtract 2x and 4 on both sides of the equation we will get
\[\Rightarrow 2x+4-2x-4=2x+4-2x-4\]
By simplifying we will get
\[\Rightarrow 0=0\]
So from the above equation we can see both the sides of the equation are equal.
So we can say that in the given equation both sides are equal.
When both the sides of the equation are equal it will be satisfied for every value of x and x can be any natural number.
From above we can say the solution for the given equation are all the natural numbers.

Note: we can also do this using distributive property. Then also we will get the same as both sides of the equation are equal. But we should know the fact that it will satisfy all the natural numbers otherwise we cannot get the answer.