Question

Solve the linear equation \[\dfrac{x}{5} = \dfrac{{x - 1}}{6}\]

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 and expressed as $ + $, 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 solution:
Since given that the equation \[\dfrac{x}{5} = \dfrac{{x - 1}}{6}\] and then we need to find the value of the unknown variable $x$, so we will make use of the basic mathematical operations to simplify further.
Starting with the cross-multiplication method we have, $\dfrac{x}{5} = \dfrac{{x - 1}}{6} \Rightarrow 6x = 5(x - 1)$
Now using the multiplication operation, we get $6x = 5x - 5$
Now during the variables on the left-hand side and also the numbers on the right-hand side we get $6x = 5x - 5 \Rightarrow 6x - 5x = - 5$ while changing the values on the equals to, the sign of the values or the numbers will change. Or we can also use the addition and subtraction as $ - 5x$ on both sides then we get $6x - 5x = 5x - 5x - 5 \Rightarrow 6x - 5x = - 5$ since equal values with opposite signs cancel each other.
Hence using the subtraction, we get $x = - 5$ and thus which is the unknown value of the given variable.

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 $ - 4x \geqslant - 8 \Rightarrow 4x \leqslant 8 \Rightarrow $ 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 $\dfrac{{6x}}{8} = \dfrac{1}{8} \Rightarrow 6x = \dfrac{1}{8} \times 8 \Rightarrow 1$
Hence using simple operations, we solved the given problem.