write the equation
Eighteen less than 6 times a number is the same as 12 more than the number.
6n - 18 = n + 12
Let's solve this step-by-step.
Let's assume the number is represented by the variable "x".
Step 1: Translate the given information into an equation.
"Eighteen less than 6 times a number" can be expressed as 6x - 18.
"12 more than the number" can be expressed as x + 12.
According to the problem statement, these two expressions are equal. Therefore, the equation is:
6x - 18 = x + 12
Step 2: Simplify the equation.
To get rid of the variables on both sides, we can subtract x from both sides:
6x - x - 18 = x - x + 12
This simplifies to:
5x - 18 = 12
Step 3: Solve for x.
To isolate the variable x on one side, we can add 18 to both sides of the equation:
5x - 18 + 18 = 12 + 18
This simplifies to:
5x = 30
Finally, to find the value of x, we divide both sides by 5:
5x/5 = 30/5
This simplifies to:
x = 6
So, the equation is 6x - 18 = x + 12 and the value of x is 6.
To write the equation, you need to break down the given information and translate it into mathematical expressions.
Let's start by assigning a variable to the unknown number.
Let's represent the unknown number by the variable "x."
Now, let's translate the given information into mathematical expressions:
"Six times a number" can be written as 6x.
"Eighteen less than 6 times a number" can be written as 6x - 18.
"12 more than the number" can be written as x + 12.
Since the problem states that "Eighteen less than 6 times a number is the same as 12 more than the number," we can set up the equation:
6x - 18 = x + 12
This equation represents the given information where "Eighteen less than 6 times a number is the same as 12 more than the number."