Question

How do you solve for x in $2x+6=10$?

Answer 1

Hint: In this question, we are given an equation in terms of x and we need to solve for x to find the value of x which satisfies the equation. For this we will try to convert the equation in the form where we have variable x on one side of the equation and a constant term on the right side of the equation. To convert the equation, we will apply operations such as addition, subtraction, multiplication, division on both sides of the equation. The value of the constant found will be the required value of x which will satisfy the equation.

Complete step by step answer:
Here we are given the equation in terms of x as $2x+6=10$.
We need to solve for x to find the value such that it satisfies the equation. For this, let us use the operation of addition, subtraction, multiplication, division on both sides of the equation such that the expression reduces to the form x = c where c is constant.
We have an equation as $2x+6=10$.
As we can see, the left side of the equation has a constant which we do not want so let us remove it. For removing 6 from the left side let us subtract 6 from both sides of the equation. We get $2x+6-6=10-6$.
Now we can see 6-6 gives 0 so we get $2x=10-6$.
Solving the subtraction between 10 and 6 on the right side of the equation we are left with 4 so we get 2x = 4.
Now as we can see the equation is not of the form x = c as we have coefficient 2 with x. So let us remove it for removing the coefficient of x, let us divide both sides by 2 we get $\dfrac{2x}{2}=\dfrac{4}{2}$.
We know 2 divided by 2 gives 1 and also 4 divided by 2 gives 2. So the equation becomes x = 2.
This equation is of the form x = c where constant becomes 2.

Therefore the value of x becomes 2 which satisfies the equation.

Note: Students should take care of the operation that they are using on both sides of the equation. Take care of the signs while solving. Students can also check their answers by following way,
For checking let us put x = 2 in the original equation $2x+6=10$ we get $2\left( 2 \right)+6=10$.
$2\times 2$ gives us 4 so the equation becomes $4+6=10\Rightarrow 10=10$.
Solving the left side we get 10 = 10.
Left side is equal to the right side, therefore the value of x as 2 satisfies the equation.