Question

How do you solve $3\left( 2z-5 \right)=2z+13$ ?

Answer 1

Hint: To solve these types of problems, we will apply the BODMAS rule. The BODMAS rule stands for Brackets Of Division Multiplication Addition Subtraction. We first open up the brackets after applying the distributive property. Then, we subtract the algebraic terms $6z,2z$ and after that the arithmetic terms $15,13$ to get the solution.

Complete step-by-step answer:
The equation that we are supposed to solve in this problem is,
$3\left( 2z-5 \right)=2z+13$
As we can see that the above equation is an equation of a single variable, which is x over here. This means that we get a definite solution from a single equation and we do not require multiple equations in order to get a solution.
In order to solve this equation, we will apply the BODMAS rule shortly. The BODMAS rule stands for Brackets Of Division Multiplication Addition Subtraction. As there are brackets in the above equation, we will solve that bracket first but, as the two terms in the brackets are different, one being algebraic and the other being arithmetic, we need to simply open up the brackets after multiplying $3$ with the terms inside the bracket. After opening up the brackets, the equation thus becomes,
 $\Rightarrow 6z-15=2z+13$
After examining the above equation, we can see that there are two algebraic terms of the same variable and having the same degree. So, we simply need to subtract them. After performing the addition, the above equation thus becomes,
$\Rightarrow 4z-15=13$
Also, there are two arithmetic terms, one being on the left-hand side and the other being on the right-hand side. So, we need to combine them by adding or subtracting them accordingly. Adding $15$ from both sides, we get,
$\Rightarrow 4z=28$
Dividing both sides by $4$ ,
$\Rightarrow z=7$
Therefore, we can conclude that the solution is $z=7$ .

Note: The distributive property must be applied correctly. For such problems which require multiplication, we need to be cautious with the terms and their signs. Also, we can solve the problem by bringing all the terms to one side of the equation and then solving accordingly, like $3\left( 2z-5 \right)-2z-13=0$ .