five times a number decreased by eight is at most ten more than twice the number
5x-8 <= 2x+10.
which way does the sign go if it says is at most
Let's break down the problem step by step:
Step 1: Let's assume the number we are working with is represented by the variable "x".
Step 2: "Five times a number" can be expressed as 5x.
Step 3: "Decreased by eight" means we subtract 8 from 5x, resulting in 5x - 8.
Step 4: "Is at most" means we use the less than or equal to symbol, which is ≤.
Step 5: "Ten more than twice the number" is represented by 10 + 2x.
Putting it all together, we can write the equation:
5x - 8 ≤ 10 + 2x
To solve this equation, we can start by isolating the x term on one side. Subtract 2x from both sides:
3x - 8 ≤ 10
Next, add 8 to both sides:
3x ≤ 18
Finally, divide both sides by 3:
x ≤ 6
Therefore, the number must be less than or equal to 6 to satisfy the given conditions.
To solve this problem, we need to translate the given sentence into a mathematical equation.
Let's start by assigning a variable to the unknown number. Let's call it "x".
The sentence "five times a number decreased by eight" can be written as "5x - 8".
The phrase "is at most ten more than twice the number" can be written as "≤ 2x + 10".
Putting it all together, the equation becomes:
5x - 8 ≤ 2x + 10
To solve for x, we can start by isolating the x term on one side of the inequality. Let's subtract 2x from both sides of the equation:
5x - 2x - 8 ≤ 2x - 2x + 10
This simplifies to:
3x - 8 ≤ 10
Next, let's isolate the constant term by adding 8 to both sides of the equation:
3x - 8 + 8 ≤ 10 + 8
Simplifying further:
3x ≤ 18
Now, to get the value of x, we divide both sides of the equation by 3:
(3x) / 3 ≤ 18 / 3
This simplifies to:
x ≤ 6
Therefore, the unknown number "x" is at most 6.