the sum of a number and fourteen is less than or equal to three times the number

x + 14 <= 3x

x - 3x <= -14
-2x <= -14
X >= 7.

Well, well, well, looks like we have a math problem here. Let's break it down, shall we?

If we have a number, let's call it "x", the sum of that number and fourteen would be "x + 14". And, according to our problem, this sum is less than or equal to three times the number, which we can express as "3x".

So, mathematically speaking, we have the inequality: x + 14 ≤ 3x.

Now, how can we solve this? Let's bring those "x" terms together and those numbers together. Subtracting "x" from both sides of the inequality gives us: 14 ≤ 2x.

Alright, let's divide everything by 2, because sharing is caring: 7 ≤ x.

So, any number that is greater than or equal to 7 will satisfy this inequality. There you have it! But remember my friend, don't take my answers too seriously, especially when you're doing your homework!

Let's represent the number with the variable "x". The problem states that "the sum of a number and fourteen is less than or equal to three times the number."

To write this algebraically, we can translate the sentence into an inequality:

x + 14 ≤ 3x

Now, let's solve for x step-by-step:

1. Subtract x from both sides of the inequality:
x + 14 - x ≤ 3x - x
14 ≤ 2x

2. Divide both sides of the inequality by 2:
14/2 ≤ 2x/2
7 ≤ x

So, the solution to the inequality is x ≥ 7. This means that any number greater than or equal to 7 satisfies the given condition.

To solve the inequality "the sum of a number and fourteen is less than or equal to three times the number," we can follow these steps:

Step 1: Assign a variable to represent the unknown number. Let's use 'x' in this case.

Step 2: Translate the given information into mathematical expressions. The sum of a number and fourteen can be written as "x + 14," and three times the number can be written as "3x."

Step 3: Write the inequality statement using the mathematical expressions. In this case, we have "x + 14 ≤ 3x."

Step 4: Solve the inequality by isolating the variable, x. Start by subtracting x from both sides of the inequality to get rid of the x term on the right side. This gives us:

x + 14 - x ≤ 3x - x

Simplifying further, we have:

14 ≤ 2x

Step 5: Finally, divide both sides of the inequality by 2 to solve for x:

14/2 ≤ 2x/2

7 ≤ x

Therefore, the solution to the inequality is x ≥ 7. This means any number that is greater than or equal to 7 will satisfy the given inequality.