twice the difference of a number and four is less than the sum of the number and five
Let x = number
2(x-4) < x+5
Solve for x.
{n|n<13} which is the same as n<13
Let's break down the given statement step-by-step:
1. Let's assume the number is represented by the variable 'x'.
2. "The difference of a number and four" can be represented as (x - 4).
3. "Twice the difference of a number and four" is therefore 2(x - 4) or 2x - 8.
4. "The sum of the number and five" can be represented as (x + 5).
5. The given statement states that "twice the difference of a number and four is less than the sum of the number and five", which can be written mathematically as:
2x - 8 < x + 5
Now, we can solve this inequality step-by-step:
6. Simplify the equation:
2x - 8 < x + 5
Subtract x from both sides:
x - 8 < 5
7. Add 8 to both sides:
x - 8 + 8 < 5 + 8
Simplify:
x < 13
Therefore, our solution is x < 13. This means that any number smaller than 13 will satisfy the given condition.
To solve this problem, we can break it down into smaller steps.
Let's assume the number we are trying to find is represented by the variable "x."
Step 1: Express the given information as an equation.
The problem states that "twice the difference of a number and four is less than the sum of the number and five."
This can be written as:
2(x - 4) < x + 5
Step 2: Simplify the equation.
Distribute the 2 on the left side of the equation:
2x - 8 < x + 5
Step 3: Isolate the variable.
To isolate the variable, we need to move all the terms containing "x" to one side of the inequality. We can do this by subtracting "x" from both sides of the equation and also adding 8 to both sides:
2x - x - 8 + 8 < x - x + 5 + 8
x < 13
Step 4: Interpret the solution.
The solution to this inequality is "x < 13." This means that any number less than 13 will satisfy the given condition.
So, the answer to the problem is that the number should be less than 13.