Question

How do you solve the linear equation $6(2x-3)=30$ ?

Answer 1

Hint: In this question, we have to find the value of x. As we have to solve a linear equation that consists of only a variable. Thus, we will apply distributive property and simple mathematical operations to get the solution to the problem. Therefore, we start solving this equation by applying the distributive property $a(b-c)=ab-ac$ and then add 18 on both sides of the equation and then we cancel out the same terms with the opposite sign on the left-hand side of the equation. Then, we will divide 12 on both sides of the equation and make necessary calculations that give the value of x, which is our required answer.

Complete step-by-step solution:
According to the question, we have to find the value of x.
The equation given to us is $6(2x-3)=30$ ---------- (1)
First, we will use the distributive property $a(b-c)=ab-ac$ in the equation (1), we get
$12x-18=30$
 Now, we will add 18 on both-hand sides of the above equation, we get
$12x-18+18=30+18$
Now, we know that the same terms with opposite signs cancel out each other, therefore we cancel the same terms on the left-hand side in the above equation, we get
$12x=48$
Now, we will divide 12 on both sides of the equation, we get
$\dfrac{12}{12}x=\dfrac{48}{12}$
On further solving the above equation, we get
$\Rightarrow x=4$ which is our required answer.

Therefore, for the equation $12x-18=30$ , the value of x is equal to $4$ , which is our required answer.

Note: Make all the necessary calculations properly and avoid mathematical errors. Do write all the steps one-by-one to avoid any confusion and mathematical errors. One of the alternative methods to solve this problem is first we will divide 6 on both sides of the equation and then, we will add 3 to the new equation. In the end, we will again divide 2 on both sides of the equation, which is our required solution to the problem.