Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four.
2(x+4) < 3(x+7) - 4
Solve for x.
2(x+4) <= 3(x+7) - 4.
2x+8 <= 3x+21 - 4
-x <= 9
Divide both sides by -1and reverse inequality sign:
X >= -9.
Two times a number decreased by three is between -33 and 33.
Well, well, well, looks like we've got ourselves a mathematical riddle! Let's break it down with a chuckle, shall we?
So, we've got "two times the sum of a number and four," which we can express as 2(x + 4). And this glorious expression has to be no more than "three times the sum of the number and seven decreased by four." That would be 3(x + 7) - 4.
Now, let's combine the humor and math magic to get our solution.
2(x + 4) ≤ 3(x + 7) - 4
Now, we can solve this inequality for x.
2x + 8 ≤ 3x + 21 - 4
Let's bring those like terms together, shaking off the extra weight.
2x - 3x ≤ 21 - 4 - 8
Oh dear, looks like a bit of subtraction shenanigans. Let's sort it out.
-x ≤ 9
Now, it's time to multiply by -1 to get rid of that sneaky negative sign.
x ≥ -9
And there you have it! The solution to this riddle is that the number has to be greater than or equal to -9.
Hope that brought a smile to your face, my friend! Feel free to ask me anything else, and I'll be here to entertain you with more humorous math mastery.
To solve this problem, let's break it down into steps:
Step 1: Define the unknown variable
Let's assume the unknown number is represented by 'x'.
Step 2: Translate the problem into an equation
The problem states that "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four." Let's break it down and translate it into an equation:
2(x + 4) ≤ 3(x + 7) - 4
Step 3: Solve the equation
Now, let's solve for 'x' using basic algebraic operations. Starting with the equation from Step 2:
2x + 8 ≤ 3x + 21 - 4
Combine like terms:
2x + 8 ≤ 3x + 17
Subtract 2x from both sides to isolate the 'x' terms on one side:
8 ≤ x + 17
Subtract 17 from both sides:
8 - 17 ≤ x
Simplify:
-9 ≤ x
So, the inequality is x ≥ -9.
Step 4: Interpret the solution
The solution, x ≥ -9, means that any number greater than or equal to -9 will satisfy the inequality. In simpler terms, any value of 'x' that is greater than or equal to -9 will make the left side (2(x + 4)) no more than the right side (3(x + 7) - 4) of the equation.