five times the number increased by thirteen is less than or equal to twice the nummmber decreased by twenty find the solution
Let the number be x
Now just translate the English to Math
5x + 13 ≤ 2x - 20
3x ≤ -33
x ≤ -11
Well, well, well, looks like we have some mathematical mischief to solve! Let's break it down, shall we?
We have the expression "five times the number increased by thirteen." So, if we let the number be 'x', we can write it as 5x + 13.
On the other side, we have "twice the number decreased by twenty." Using the same 'x', this expression becomes 2x - 20.
Now, we need to find when the first expression is less than or equal to the second expression. In other words, we need to solve the inequality:
5x + 13 ≤ 2x - 20
Time for some funny business with numbers! Let's isolate the 'x' term by subtracting 2x from both sides:
5x - 2x + 13 ≤ 2x - 2x - 20
Simplifying gives us:
3x + 13 ≤ -20
Oh boy, oh boy, negative numbers playing tricks on us! To get rid of that cheeky 13 on the left side, we're gonna subtract 13 from both sides:
3x + 13 - 13 ≤ -20 - 13
Simplifying again, we have:
3x ≤ -33
Now, we want to know the solution, right? Dividing both sides by 3 (and being super careful not to divide by zero like a clumsy mathematician) gives us:
x ≤ -11
So, the solution to the inequality is that the number 'x' is less than or equal to -11.
I hope that helps light up your mathematical journey with a chuckle or two! If you have any more questions, just ask!
Let's break down the given information into an equation:
"Five times the number increased by thirteen" can be represented as 5x + 13, where x is the unknown number.
"Twice the number decreased by twenty" can be represented as 2x - 20.
According to the problem, 5x + 13 is less than or equal to 2x - 20. This can be written as:
5x + 13 ≤ 2x - 20
To solve this equation, let's isolate the x variable. Subtracting 2x from both sides of the equation gives:
5x - 2x + 13 ≤ 2x - 2x - 20
Simplifying further:
3x + 13 ≤ -20
Subtracting 13 from both sides of the equation:
3x + 13 - 13 ≤ -20 - 13
3x ≤ -33
Finally, dividing both sides of the equation by 3 gives:
x ≤ -33/3
So, the solution to the given inequality is:
x ≤ -11
To find the solution to the given inequality, let's break down the problem into smaller steps.
Step 1: Understand the Given Information
The problem states that "five times the number increased by thirteen is less than or equal to twice the number decreased by twenty."
Step 2: Translate the Given Information into an Inequality
Let's assign a variable to represent the number. Let's call it "x."
"Five times the number increased by thirteen" can be translated as 5x + 13.
"Twice the number decreased by twenty" can be translated as 2x - 20.
Now we can write the inequality as 5x + 13 ≤ 2x - 20.
Step 3: Solve the Inequality
To solve the inequality, we need to isolate the variable on one side.
First, we can isolate the x terms by subtracting 2x from both sides:
5x - 2x + 13 ≤ -20.
Combining like terms, we have:
3x + 13 ≤ -20.
Next, we isolate the constant term by subtracting 13 from both sides:
3x + 13 - 13 ≤ -20 - 13.
Simplifying further, we obtain:
3x ≤ -33.
Finally, we can isolate the variable by dividing both sides by 3:
3x/3 ≤ -33/3.
Simplifying the expression, we have:
x ≤ -11.
So, the solution to the given inequality is x ≤ -11.