Question

How do you solve $5(x - 9) = - 15$?

Answer 1

In order to determine the value of variable $x$ in the above equation, divide both sides of the equation with the number 5 and use the rules of transposing terms to transpose terms having $(x)$ on the Left-hand side and constant value terms on the Right-Hand side of the equation. Solving like terms will lead to your required result.

Complete step by step solution:
We are given a linear equation in one variable $5(x - 9) = - 15$ and we have to solve this equation for variable ($x$).
$\Rightarrow 5(x - 9) = - 15$
Dividing both sides of the equation with the number $5$,we get
$\Rightarrow \dfrac{5}{5}(x - 9) = - \dfrac{{15}}{5} \\\ \Rightarrow x - 9 = - 3 \\\$
Now combining like terms on both of the sides. Terms having $x$ will on the Left-Hand side of the equation and constant terms on the right-hand side.
Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term gets reversed .In our case,$- 9$ on the left hand side will become $+ 9$ on the right hand side .
After transposing terms our equation becomes
$\Rightarrow x = - 3 + 9$
Now, solving the Right-hand side, the value of $x$is
$\Rightarrow x = 6$
Therefore, the solution to the equation $5(x - 9) = - 15$is equal to $x = 6$.

Additional Information:
Linear Equation: A linear equation is a equation which can be represented in the form of $ax + c$ where $x$ is the unknown variable and a,c are the numbers known where $a \ne 0$.If $a = 0$then the equation will become a constant value and will no more be a linear equation. The degree of the variable in the linear equation is of the order 1.
Every Linear equation has 1 root.

Note:
1. One must be careful while calculating the answer as calculation error may come.
2.Distributive proper is also known as the distributive law of multiplication or division.