three times the sum of a number and six is greater than four times the number decreased by two
3(x+6) > 4(x-2)
x is the number your looking for
since it says greater than you need to place an inequalities sign
above is how it should look just solve to get x by itself
good luck
20
Why did six feel so threatened by the number? Because the number was "summing" up to trouble!
In this case, we have the inequality:
3(n + 6) > 4n - 2
Let's simplify it with some goofy math:
3n + 18 > 4n - 2
Now, let's get all the number terms to one side and the constant terms to the other side:
3n - 4n > -2 - 18
Naturally, subtracting numbers is as easy as herding cats, so we get:
-n > -20
And since we want the number to be positive, let's multiply the entire equation by -1:
n < 20
So, the number is less than 20. Keep it away from any complicated equations, it seems to get easily overwhelmed!
Let's break down the problem step by step:
Step 1: Define the variables.
Let's represent the number as "x".
Step 2: Identify the given information.
The given information states that three times the sum of a number and six is greater than four times the number decreased by two.
Step 3: Translate the given information into an equation.
Three times the sum of a number (3 * (x + 6)) is greater than four times the number decreased by two (4x - 2).
Step 4: Write the equation.
3(x + 6) > 4x - 2
Step 5: Solve the equation.
Distribute the 3 on the left side of the equation:
3x + 18 > 4x - 2
Subtract 3x from both sides:
18 > x - 2
Add 2 to both sides:
20 > x
So, the solution is x < 20.
To summarize, the inequality is x < 20, which means that any number less than 20 will satisfy the given condition.
To solve this problem, let's break it down into smaller steps.
Let's assume the number we're trying to find is "x."
The problem states that "three times the sum of a number and six is greater than four times the number decreased by two."
Let's translate this into an equation:
3(x + 6) > 4x - 2
Now, let's solve for x:
First, distribute 3 to the terms inside the parentheses:
3x + 18 > 4x - 2
Next, let's move all the terms with "x" to one side of the equation and the constant terms to the other side:
3x - 4x > -2 - 18
Simplifying further:
-x > -20
To solve for x, we need to change the direction of the inequality by multiplying both sides by -1. Remember, when you multiply or divide an inequality by a negative number, the direction of the inequality sign is reversed:
(-1)(-x) < (-1)(-20)
Simplifying this gives us:
x < 20
So, the original number is less than 20.