Question

Find $x$ in $\dfrac{{2x + 5}}{3} = 3x - 10$.

Answer 1

Hint:Take the given expression and will perform the cross multiplication where the denominator of one side is multiplied with the numerator of the opposite side and then will simplify the equation for the value of “$x$”.

Complete step by step answer:
Take the given expression: $\dfrac{{2x + 5}}{3} = 3x - 10$
Perform cross multiplication in the above equation –
$2x + 5 = 3(3x - 10)$
Multiply the term inside the bracket with the term outside the bracket.
$2x + 5 = 9x - 30$
The above equation can be re-written as –
$9x - 30 = 2x + 5$
Make like terms together, move terms with “$x$” on the left hand side of the equation and the constant on the right hand side of the equation. When you move any term from one side of the equation to the opposite side then the sign of the terms also changes. Positive term becomes negative and vice versa.
$9x - 2x = 5 + 30$

Simplify the above expression finding the difference and sum of the terms on both sides of the equation.
$7x = 35$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$x = \dfrac{{35}}{7}$
Find the factors for the above term in the denominator.
$x = \dfrac{{7 \times 5}}{7}$
Common factors from the denominator and the numerator cancel each other.
$ \therefore x = 5$
This is the required solution.

Hence, the value of $x$ is $\dfrac{{7 \times 5}}{7}$.

Note: Be careful about the sign convention while opening the brackets. When there is positive sign outside the bracket then the sign of the terms remains the same while when there is negative sign outside the bracket then the sign of the term inside the bracket changes when open. Positive term becomes negative and vice-versa.