Question

How do you solve $\dfrac{{3x - 4}}{5} = 7$?

Answer 1

Hint: We will use the cross formula to rearrange the given equation and then we will take the like terms together and then simplify them to get the final value of $x$.

Complete step-by-step solution:
The given equation is: $\dfrac{{3x - 4}}{5} = 7$
On cross multiplying the terms on the right-hand side we get: $3x - 4 = 7 \times 5$
On simplifying the right-hand side, we get: $3x - 4 = 35$
Now on transferring the term $ - 4$ across the $ = $ sign we get: $3x = 35 + 4$
On simplifying we get: $3x = 39$
Dividing both the sides by $3$ and we get:
$ \Rightarrow \dfrac{{3x}}{3} = \dfrac{{39}}{3}$
On simplifying we get:
$\Rightarrow$$x = 13$

The value of x is equal to 13.

Note: It is to be remembered that while cross multiplying when a term which is multiplication and division will change into division and multiplication respectively.
Similarly, when a term which is positive or negative when transferred across the $ = $ sign will become negative or positive respectively.
The cross formula is used to simplify the terms because an equation which has two fractions, their value won’t be changed if they are multiplied or divided by the name number.
The cross formula is also used to find out the missing value of a term by considering it to be $x$.
It is to be remembered that the denominator of a fraction cannot be zero because division by zero is unacceptable in mathematics.
The main reason for using cross multiplication is to compare the fractions, it tells us which fraction is greater and which one is smaller. It is useful when working with large fractions which are complex to reduce.