Question

Solve $5x - \dfrac{1}{3}(x + 1) = 6(x + \dfrac{1}{{30}})$

Answer 1

Hint: The addition is the sum of given two or more than two numbers, or variables and in addition, if we sum the two or more numbers then we obtain a new frame of the number will be found, also in subtraction which is the minus of given two or more than two numbers, but here comes with the condition that in subtraction the greater number sign represented in the number will stay constant example $2 - 3 = - 1$

Complete step by step answer:
Since given that the equation $5x - \dfrac{1}{3}(x + 1) = 6(x + \dfrac{1}{{30}})$ and we need to find the unknown variable value of the $x$
Starting the simplification using the cross multiplication we get $\dfrac{{3 \times 5x - (x + 1)}}{3} = 6(\dfrac{{30 \times x + 1}}{{30}})$
Now using the multiplication operation, we get $\dfrac{{3 \times 5x - (x + 1)}}{3} = 6(\dfrac{{30 \times x + 1}}{{30}}) \Rightarrow \dfrac{{15x - (x + 1)}}{3} = \dfrac{{180x + 6}}{{30}}$
Now using the subtraction operation, we have $\dfrac{{15x - x - 1}}{3} = \dfrac{{180x + 6}}{{30}} \Rightarrow \dfrac{{14x - 1}}{3} = \dfrac{{180x + 6}}{{30}}$
Again, cross multiplication we have $\dfrac{{14x - 1}}{3} = \dfrac{{180x + 6}}{{30}} \Rightarrow 30(14x - 1) = 3(180x + 6)$
Again, by the multiplication operation, we get $420x - 30 = 540x + 18$
Now Turing the variables on the left-hand side and also the numbers on the right-hand sides we get $420x - 540x = 18 + 30$ (the signs will change)
Now by the subtraction and addition operation, we get $ - 120x = 48$
Hence by division, we get $x = - \dfrac{{48}}{{120}} = - \dfrac{2}{5}$
Thus, we have the unknown variable as $x = - \dfrac{2}{5}$ or $x = - 0.4$

Note:
The other two operations are multiplication and division operations.
Since multiplicand refers to the number multiplied. Also, a multiplier refers to multiplying the first number. Have a look at an example; while multiplying $5 \times 7$the number $5$ is called the multiplicand and the number $7$ is called the multiplier. Like $2 \times 3 = 6$ or which can be also expressed in the form of $2 + 2 + 2(3times)$
The process of the inverse of the multiplication method is called division. Like $x \times y = z$is multiplication thus the division sees as $x = \dfrac{z}{y}$. Like $x = - \dfrac{{48}}{{120}} = - \dfrac{2}{5}$
Hence using simple operations, we solved the given problem.