Question

Solve the following: 4(2-x)=8

Answer 1

Hint: In this question, we have been given an equation, which we can solve by dividing both sides of the equation by -4 to find the value of (x-2) and finally adding 2 to both sides of the equation to get the value of x. Thereafter, we can put the obtained value of x in the LHS and then verify that the value in LHS equals that in RHS.

Complete step-by-step answer:

The given equation is
 \[4\left( 2-x \right)=8\]
Now, we will divide both sides of the equation by $-4$ , and we know that if we divide both sides of an equation by a real number other than zero, the equation will hold true.
\[\dfrac{4}{-4}\left( 2-x \right)=\dfrac{8}{-4}\]
\[\Rightarrow -\left( 2-x \right)=-2\]
Now, we will multiply the negative sign and open the bracket. On doing so, we get
\[-2+x=-2\]
We know that an equation remains valid if we add or subtract the same number both in the Left Hand Side (LHS) and Right Hand Side (RHS). Therefore, we should add a number on both sides such that only x remains on the LHS. As -2 is present as a separate term in LHS, we will add 2 to both sides in equation to obtain
$-2+x+2=-2+2$
$\Rightarrow x=0$
Therefore, the value of x that satisfies the equation \[4\left( 2-x \right)=8\] is x=0.

Note: Be careful about the calculation and the signs while opening the brackets. Instead of dividing the equation by -4, we can also divide by 4 and solve as usual. The general mistake that a student can make is \[-\left( 2-x \right)=-2-x\] . If you do this, you will still get the right answer, but the method is wrong and will result in loss of marks. Also, you should remember that multiplying, adding, subtracting, or dividing the LHS and RHS of an equation by the same number gives other equation which is true, however you should not divide both sides of an equation by 0, as that would give non determinate values on the both sides of the equation.