Question

Solve for the value of x from the following: $0.3\left( {6 - x} \right) = 0.4\left( {x + 8} \right)$

Answer 1

Hint: Here we have to find the value of the variable \[x\] by simplifying both sides of the given equation. First, we will simplify it by multiplication. In this, we have given 0.3 and 0.4 these are rational numbers written in a decimal form.
We can write these decimal forms in rational numbers like as,
$0.3 = \dfrac{3}{{10}}$& $0.4 = \dfrac{4}{{10}}$

Complete step-by-step solution:
By the hint let us replace 0.3 by 3/10 and 0.4 by 4/10.
$ \Rightarrow \dfrac{3}{{10}}\left( {6 - x} \right) = \dfrac{4}{{10}}\left( {x + 8} \right)$
To simplify here we have to do multiplication.
$ \Rightarrow \left( {\dfrac{3}{{10}} \times 6} \right) - \dfrac{{3x}}{{10}} = \dfrac{{4x}}{{10}} + \left( {\dfrac{4}{{10}} \times 8} \right)$
 $ \Rightarrow \dfrac{{18}}{{10}} - \dfrac{{3x}}{{10}} = \dfrac{{4x}}{{10}} + \dfrac{{32}}{{10}}$
Now put variable terms in one side and constant terms on the other side.
$\therefore - \dfrac{{3x}}{{10}} - \dfrac{{4x}}{{10}} = \dfrac{{32}}{{10}} - \dfrac{{18}}{{10}}$
Here denominators are the same so we will do the operations with numerators and keep the denominator as it is.
$\therefore - \dfrac{{7x}}{{10}} = \dfrac{{14}}{{10}}$
We have to find the value of x.
$ - \dfrac{7}{{10}}$ is multiplied to x. So, for simplification, we will divide it to$\dfrac{{14}}{{10}}$.
$ \Rightarrow - x = \dfrac{{\dfrac{{14}}{{10}}}}{{\dfrac{7}{{10}}}}$
Simplify it.
$ \Rightarrow - x = \dfrac{{14}}{{10}} \times \dfrac{{10}}{7}$
10 will get canceled.
So, we will get.
$\therefore - x = \dfrac{{14}}{7}$
$ \Rightarrow - x = 2$
Multiply by minus sign on the both sides.
$\therefore - \left( { - x} \right) = - 2$
$\therefore x = - 2$

So, the value of x is -2.

Note: A rational number is a number that can be expressed as the fraction p/q of two integers, a numerator p, and the non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by Q. It was denoted in 1895 by Giuseppe.
The set of all rational numbers is countable. The results are always rational numbers if we multiply, add or subtract any two rational numbers. A rational number remains the same if we divide or multiply both the numerator and denominator with the same factor.