what is two more than a number equals three times the sum of one-third of the number plus 6 in standard or numerical form.
2x = 3(1/3x + 6)
2x = x + 18
x = 18
The question is bogus, there is no solution
Sierra read your question as "two times a number" but you said "two more than a number" , so it should be
x - 2 = 3((1/3)x + 6)
x-2 = x + 18
-2 = 18 , makes no sense !
To solve the problem, let's break it down step by step:
Step 1: Let's assign a variable to represent the unknown number. Let's call it "x". So, the number is "x."
Step 2: Translate the given information into an equation.
The problem states that "two more than a number" is equal to "three times the sum of one-third of the number plus 6."
The first part, "two more than a number," can be written as: "x + 2."
The second part, "three times the sum of one-third of the number plus 6," is: "3 * ((1/3) * x + 6)."
Putting it together, we have the equation: x + 2 = 3 * ((1/3) * x + 6).
Step 3: Simplify the equation.
Start by simplifying the expression inside the parentheses:
(1/3) * x + 6 = (x/3) + 6.
Now, substitute this simplified expression back into the equation:
x + 2 = 3 * ((x/3) + 6).
Next, simplify the right-hand side (RHS) of the equation:
3 * ((x/3) + 6) = 3 * (x/3) + 3 * 6 = x + 18.
So, the equation becomes: x + 2 = x + 18.
Step 4: Solve the equation.
To solve for "x," we can start by isolating the variable on one side of the equation. Let's move "x" to the left side and "2" to the right:
x - x = 18 - 2.
This simplifies to: 0 = 16.
However, we have a contradiction: 0 cannot equal 16. Therefore, there is no solution to this equation.
In standard or numerical form, we can write the final answer as: There is no number that satisfies the given conditions.