Question

How do you solve $50=15-6\left( 2x-5 \right)$?

Answer 1

Hint: We have a linear equation in one variable. We will solve this linear equation in one variable to obtain the solution of the equation. We will use the distributive property of to simplify the given equation. We will shift all the constant terms on one side of the equation. Then we will divide both sides of the equation by the coefficient of the variable. After that, we will get the value of the variable.

Complete step by step answer:
The given equation is $50=15-6\left( 2x-5 \right)$. We have to solve this linear equation in one variable to obtain the solution of this equation. Since it is only one linear equation and it has only one variable, there is only one solution to this equation.
Let us simplify the given equation using the distributive property. The distributive property states that multiplying the sum of two or more terms by a number will give the same result as multiplying each term individually by the number and then adding the products together. So, we can write $-6\left( 2x-5 \right)=\left( -6 \right)\left( 2x \right)-\left( -6 \right)\left( 5 \right)$. So, we get the following equation,
$50=15+\left( -6 \right)\left( 2x \right)-\left( -6 \right)\left( 5 \right)$
Simplifying the above equation, we get
$50=15-12x+30$
Let us shift the constant terms to one side of the equation. We will shift the constant terms to the left hand side, which does not have any term with the variable. So, we get the following equation,
$50-15-30=-12x$
We know that $50-15-30=5$. Therefore, we can write the above equation as
$-12x=5$
Now, we will divide both sides of the equation by the coefficient of the variable, which is $-12$. So, we get the following,
\[\begin{align}
  & \dfrac{-12x}{-12}=\dfrac{5}{-12} \\
 & \therefore x=-\dfrac{5}{12} \\
\end{align}\]

Therefore, we have obtained $x=-\dfrac{5}{12}$ as the solution of the given linear equation.

Note: An equation can be classified by looking at the number of variables and the degree of the equation. The degree of the equation is the highest power of the variables in one term. The key point in this question is the use of the distributive property. This property gives a relation between two binary operations, multiplication and addition. We can verify the answer by substituting the obtained value of x in the equation and checking if RHS=LHS.