Question

How do you solve $2\left( 3x-1 \right)+2\left( 4x+5 \right)=8$?

Answer 1

Hint: Now to solve the equation we will first open the brackets and simplify the equation. Now we will rearrange the terms such that the variables and constants are separated. Now we will divide the whole equation by coefficient of x and hence find the solution of the equation.

Complete step-by-step answer:
Now consider the given equation $2\left( 3x-1 \right)+2\left( 4x+5 \right)=8$
We can see that the given equation is a linear equation in x. Now to solve the equation we need to find the value of x for which the equation holds.
Now first we will open the brackets using distributive property. We know that the distributive property states that $a\left( b+c \right)=ab+ac$ . Hence using this we get,
$\Rightarrow 6x-2+8x-10=8$
Now rearranging the terms in the equation we get,
$\Rightarrow 6x+8x-2-10=8$
Now we know that we can add and subtract the terms with the same variables and powers. Hence we have 6x + 8x = 14x. Using this we get,
$\Rightarrow 14x-12=8$
Now adding 12 on both sides of the equation we get,
$\begin{align}
  & \Rightarrow 14x=12+8 \\
 & \Rightarrow 14x=20 \\
\end{align}$
Now let us divide the equation by the coefficient of x which in this case is 14. Hence we get the solution of the equation is $x=\dfrac{20}{14}$
Now reducing the fraction to its lowest form by dividing the numerator and denominator by 2 we get, $x=\dfrac{10}{7}$
Hence the solution of the given equation is $x=\dfrac{10}{7}$.

Note: Now note that when we solve an equation for solution we can always check the solution by substituting the value obtained in the equation. The solution is correct if the equation holds on substituting the value in the equation.