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Question: How do you solve \(5(x - 9) = - 15\)?...

How do you solve 5(x9)=155(x - 9) = - 15?

Explanation

Solution

In order to determine the value of variable xx 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)(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(x9)=155(x - 9) = - 15 and we have to solve this equation for variable (xx).
5(x9)=15\Rightarrow 5(x - 9) = - 15
Dividing both sides of the equation with the number 55,we get
55(x9)=155 x9=3  \Rightarrow \dfrac{5}{5}(x - 9) = - \dfrac{{15}}{5} \\\ \Rightarrow x - 9 = - 3 \\\
Now combining like terms on both of the sides. Terms having xx 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 - 9 on the left hand side will become +9 + 9 on the right hand side .
After transposing terms our equation becomes
x=3+9\Rightarrow x = - 3 + 9
Now, solving the Right-hand side, the value of xxis
x=6\Rightarrow x = 6
Therefore, the solution to the equation 5(x9)=155(x - 9) = - 15is equal to x=6x = 6.

Additional Information:
Linear Equation: A linear equation is a equation which can be represented in the form of ax+cax + c where xx is the unknown variable and a,c are the numbers known where a0a \ne 0.If a=0a = 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.