Question

How do you solve $x-2\left( x+10 \right)=12$?

Answer 1

Hint: We will see the distributive property that involves the operations multiplication and addition. Then we will use this property to simplify the given equation. After simplification, we will obtain a linear equation in one variable. We will rearrange this equation so that we have the variable terms on one side and the constant terms on the other. Then we will solve this equation to obtain the value of the variable.

Complete step-by-step answer:
The given equation is $x-2\left( x+10 \right)=12$. Now, according to the BODMAS rule, we should first address the bracket in the expression. We can see that the terms inside the bracket are being multiplied by 2. We have the distributive property to simplify such cases. 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. This means we have $a\left( b+c \right)=ab+ac$. Using the distributive property, we can write the given equation in the following manner,
$\begin{align}
  & x-2x-2\times 10=12 \\
 & \therefore x-2x-20=12 \\
\end{align}$
Now, we can see that the above equation is a linear equation in one variable. We will rearrange the equation so that we have the terms with variables on one side and the constant terms on the other side. So, we have the following,
$x-2x=12+20$
Solving the above equation for $x$, we get
$\begin{align}
  & -x=32 \\
 & \therefore x=-32 \\
\end{align}$

Note: We should be familiar with the properties like distributive property, commutative property and associative property. These properties are very useful for simplification and solving of equations. Linear equations are the equations that have the highest degree of any term as 1. When the highest degree of any term in an equation is 2, it is a quadratic equation.