Question

How do you solve $2\left( x-4 \right)+2x=-6x-2$ ?

Answer 1

Hint: At first, we apply distributive property to the left hand side of the equation. We then bring all the $x-terms$ on the left hand side and the arithmetic terms to the other side. We can now easily solve for $x$ .

Complete step-by-step solution:
The given equation is
$2\left( x-4 \right)+2x=-6x-2$
As we see terms within brackets on the left hand side of the equation, we apply distributive property to the left hand side of the equation, that is, we multiply $2$ with the terms inside the bracket and then remove the brackets. The equation thus becomes,
$\Rightarrow 2x-8+2x=-6x-2$
We perform simplification on the left hand side of the equation. The equation thus becomes,
$\Rightarrow 4x-8=-6x-2$
We now add $6x$ to both sides of the above equation. The equation thus becomes,
$\Rightarrow 4x+6x-8=-2$
Further simplification by adding the first two terms on the left hand side of the above equation makes the equation as,
 $\Rightarrow 10x-8=-2$
Adding $8$ to both sides of the above equation, we get
$\Rightarrow 10x=8-2$
Further simplification by subtracting the two terms on the right hand side of the above equation makes the equation as,
$\Rightarrow 10x=6$
We now divide the two sides of the above equation by $10$ . The equation thus becomes,
$\Rightarrow x=\dfrac{6}{10}$
Therefore, we can conclude that the solution of the given equation is $x=\dfrac{6}{10}$.

Note: We should be careful while applying the distributive property and while interchanging the terms from one side of the equation to another. We can also solve the problem by the graphical method. We treat the two sides of the given equation as two separate equations. Then, we draw the two equations which are straight lines, on a graph paper. The point where these two lines intersect, will be the solution of the given equation.