5 times the difference of a number and 9 is 1 less than three times the same number
5(x-9) = 3x - 1
5x - 45 = 3x - 1
2x = 44
x = 22 <----- I assume you wanted the number
difference between 22 and 9 = 13
5 times that is 65
3 times the number = 66
and sure enough, 65 is 1 less than 66
x = number
5 times the difference of a number and 9 is 1 less than three times the same number means:
5 ∙ ( x - 9 ) = 3 x - 1
5 x - 45 = 3 x - 1
Add 45 to both sides
5 x = 3 x + 44
Subtract 3 x to both sides
2 x = 44
x = 44 / 2
x = 22
To solve this problem, let's break it down into steps:
Step 1: Let's assign a variable to the unknown number. Let's call it "x".
Step 2: Translate the given information into an equation. The problem states that "5 times the difference of a number and 9 is 1 less than three times the same number." We can write this as the equation:
5(x - 9) = 3x - 1
Step 3: Simplify the equation by applying the distributive property.
5x - 45 = 3x - 1
Step 4: Rearrange the equation to isolate the variable term on one side.
5x - 3x = -1 + 45
2x = 44
Step 5: Solve for x by dividing both sides of the equation by 2.
2x/2 = 44/2
x = 22
Step 6: Check the solution by substituting the value of x into the original equation.
5(22 - 9) = 3(22) - 1
5(13) = 66 - 1
65 = 65
Since both sides of the equation are equal, the solution x = 22 is correct.
So, the unknown number is 22.