Question

How do you solve the given equation $-5\left( 2x-6 \right)+8x=22$?

Answer 1

Hint: We start solving the problem by applying the distributive property $a\left( b+c \right)=ab+ac$ in the given equation. We then make the necessary calculations and then subtract 30 from the both sides of the resultant equation. We then make the necessary calculations and divide both sides of the obtained equation with –2 to get the required solution for the given equation.

Complete step by step answer:
According to the problem, we are asked to solve the given equation $-5\left( 2x-6 \right)+8x=22$.
We have given the equation $-5\left( 2x-6 \right)+8x=22$ ---(1).
From distributive property, we know that $a\left( b+c \right)=ab+ac$. Let us use this result in equation (1).
$\Rightarrow -5\left( 2x \right)-5\left( -6 \right)+8x=22$.
$\Rightarrow -10x+30+8x=22$.
$\Rightarrow -2x+30=22$ ---(2).
Let us subtract 30 from both sides of the equation (2).
$\Rightarrow -2x+30-30=22-30$.
$\Rightarrow -2x=-8$ ---(3).
Let us divide both sides of the equation (3) with –2.
$\Rightarrow \dfrac{-2x}{-2}=\dfrac{-8}{-2}$.
$\Rightarrow x=4$.
So, we have found the solution of the given equation $-5\left( 2x-6 \right)+8x=22$ as $x=4$.

$\therefore $ The solution of the given equation $-5\left( 2x-6 \right)+8x=22$ is $x=4$.

Note: Whenever we get this type of problem, we should always try to make the necessary calculations in the given equation to get the final value for x which will be the required answer. We can also solve this problem by making use of trial and error methods for the values of x in the given equation. We should not confuse while performing calculations related to sign convention. Similarly, we can expect problems to find the solution for the equation $-7\left( x-6 \right)+x=6$.