Question

How do you solve the equation $-4\left( 2x-1 \right)=-6\left( x+2 \right)-2$ .

Answer 1

Hint: Now to solve the equation we will first use the distributive property $a.\left( b+c \right)=ab+ac$ and open the brackets. Now we will bring all the variables on one side and all the constants on other sides and then simplify. Now we will divide the equation by the current coefficient of x to find the value of x.

Complete step-by-step solution:
Now let us consider the given equation $-4\left( 2x-1 \right)=-6\left( x+2 \right)-2$
We can see that the given equation is a linear equation in one variable. Now we want to find the solution of the equation hence we want to find the value of x such that it satisfies the whole equation.
Now to do so we will simplify the equation and try to write it in the form $ax=b$
Now consider $-4\left( 2x-1 \right)=-6\left( x+2 \right)-2$
We know that according to distributive property we have $a.\left( b+c \right)=a.b+a.c$
Hence using this property we get,
$\begin{align}
  & \Rightarrow -4\left( 2x \right)-4\left( -1 \right)=-6x+\left( -6 \right)\left( 2 \right)-2 \\
 & \Rightarrow -8x+4=-6x-12-2 \\
 & \Rightarrow -8x+4=-6x-14 \\
\end{align}$
Now let us transpose the term 6x on LHS and the term 4 on RHS. Hence we get,
$\Rightarrow -8x+6x=-14-4$
Now on simplifying the above equation we get,
$\Rightarrow -2x=-18$
Now dividing the whole equation by – 2 we get,
$\Rightarrow x=\dfrac{-18}{-2}=9$
Hence the solution of the given equation is x = 9.

Note: Now note that while simplifying the terms we can add and subtract the terms which are of same variables and powers. Hence we can add 2x and 5x by not $2x$ and $5{{x}^{2}}$ or 2x and 3y. Also note that while transposing the term to the opposite side the sign of term changes. Hence – 6x becomes + 6x and + 4 becomes – 4.