three less than twice a number is the same as the number increased by eight
"expressions" is a school subject I've never heard of. And what is your question here? You have made a statement. It's not a question.
Rephrasing your sentence in the language of "math" would have been easier ...
2x - 3 = x+8
To solve this problem, we need to translate the given sentence into an equation. Let's break it down step by step.
Step 1: Assign a variable to the number.
Let's assume the number is "x."
Step 2: Translate "three less than twice a number" into an equation.
"Three less than" means subtracting 3 from something.
"Twice a number" means multiplying the number by 2.
So, "three less than twice a number" can be written as "2x - 3."
Step 3: Translate "the number increased by eight" into an equation.
"The number" is the variable "x."
"Increased by eight" means adding 8 to something.
So, "the number increased by eight" can be written as "x + 8."
Step 4: Set up the equation.
The equation to represent the problem is:
2x - 3 = x + 8
Step 5: Solve the equation.
To solve for x, let's isolate the variable on one side of the equation.
2x - 3 = x + 8
Subtract x from both sides:
2x - x - 3 = x - x + 8
Simplify:
x - 3 = 8
Add 3 to both sides:
x - 3 + 3 = 8 + 3
Simplify:
x = 11
Step 6: Verify the solution.
Plug the value of x (11) back into the original equation and see if both sides are equal.
2x - 3 = x + 8
2(11) - 3 = 11 + 8
22 - 3 = 19
19 = 19
Since both sides are equal, the solution x = 11 is correct.
Therefore, the number we are looking for is 11.