Question

How do you solve $5\left( 4+2x \right)-\left( 8x-12 \right)=68$?

Answer 1

We will first simplify the given equation. We will simplify the equation by using the distributive property. We will look at the distributive property. After we obtain the simplified equation, we will rearrange the terms in the equation so that we have the constant terms on one side of the equation and the variable terms on the other side of the equation. Then we will solve the equation for the variable $x$.

Complete answer:
The given equation is $5\left( 4+2x \right)-\left( 8x-12 \right)=68$. We will simplify the equation by opening the brackets. Let us look at 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. This means that $a\left( b+c \right)=ab+ac$.
Using this property, we can open the brackets in the given equation in the following manner,
$20+10x-8x+12=68$
Now, we will rearrange the terms in the above equation so that we have the constant terms on one side of the equation and the variable terms on the other side of the equation. So, we get the following equation,
$10x-8x=68-20-12$
Solving the above equation by doing the arithmetic operations on both the sides, we get the following,
$\begin{aligned} & 2x=36 \\\ & \therefore x=18 \\\ \end{aligned}$
Therefore, the solution of the given equation is $x=18$.

Note: We should be familiar with the distributive property, associative property, commutative property. These properties are useful in simplifying equations. We should be careful with the signs of the terms while shifting them from one side to another. Since the equation we have is a linear equation in one variable, we expect it to have only one solution.