Question

How do you solve $5x-2\left( 7x+1 \right)=14x$?

Answer 1

Hint: We will look at the distributive property. We will use this law and simplify the given equation. After that we will shift the constant terms to one side of the equation and collect the terms with the variable $x$ on the other side of the equation. We will solve this equation for the variable $x$ and obtain its value.

Complete step-by-step solution:
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. That means, $a\left( b+c \right)=ab+ac$. The given equation is $5x-2\left( 7x+1 \right)=14x$. We will use the distributive property and open the bracket in the following manner,
$5x-2\cdot 7x-2\cdot 1=14x$
Simplifying this equation, we get the following,
$5x-14x-2=14x$
Now, we will collect the terms with the variable $x$ on one side of the equation and the constant terms on the other side. We will rearrange the equation in the following manner,
$5x-14x-14x=2$
Simplifying and solving the above equation for the variable $x$, we get
$\begin{align}
  & -23x=2 \\
 & \therefore x=-\dfrac{2}{23} \\
\end{align}$

Note: We have a linear equation in one variable. The graph of a linear equation is a straight line and the solution of the equation is the point where the line intersects the x-axis. We should be careful while rearranging the terms in the equation so that we can avoid minor mistakes like misplaced signs of the terms. It is important to understand the usefulness of the distributive property for simplification of such equations.