what is three less than 11 times a number is the same as the number decreased by 13. find the number
11n - 3 = n - 13
10n = -10
n = -1
Let's solve the problem step-by-step:
1. Let's assume the number is represented by 'x'.
2. According to the problem, "three less than 11 times a number" can be written as (11x - 3).
3. Also, "the number decreased by 13" can be written as (x - 13).
4. According to the problem, these two expressions are equal: (11x - 3) = (x - 13).
5. Now we can solve the equation:
11x - 3 = x - 13
6. We can simplify the equation by subtracting 'x' from both sides:
11x - x = -13 + 3
7. Simplifying further, we have:
10x = -10
8. To isolate 'x', we divide both sides by 10:
x = -10 / 10
9. Simplifying the division we get:
x = -1
So, the number is -1.
To solve this problem, we can break it down into smaller steps:
Let's assume that the number is represented by "x".
Step 1: Translate the first part of the problem into an equation.
"Three less than 11 times a number" can be expressed as:
11x - 3.
Step 2: Translate the second part of the problem into an equation.
"The number decreased by 13" can be expressed as:
x - 13.
Step 3: Set up an equation that equates the two expressions from Step 1 and Step 2.
Therefore, we have:
11x - 3 = x - 13.
Now, we can solve this equation to find the value of x.
Step 4: Simplify the equation by combining like terms.
11x - x = -13 + 3.
10x = -10.
Step 5: Solve for x by dividing both sides of the equation by 10.
x = -10/10.
Step 6: Simplify the expression to get the final answer.
x = -1.
Therefore, the number is -1.