eight times the difference of a number and three is equal to six times the sum of a number and one

8(x+3)=6(x+1)

is this right?

close, but "difference" implies subtraction

so "eight times the difference of a number and 3 --- 8(x-3)

so ...

8(x-3) = 6(x+1)

thank you!

No, the equation you wrote is not correct. Here's the correct equation:

8(x - 3) = 6(x + 1)

Let's break it down step by step:

Step 1: Start with the given information:

"Eight times the difference of a number and three is equal to six times the sum of a number and one."

Step 2: Assign variables:

Let x represent the number.

Step 3: Translate the given information into an equation:

"Eight times the difference of a number and three" can be written as 8(x - 3).

"Six times the sum of a number and one" can be written as 6(x + 1).

So the equation becomes:

8(x - 3) = 6(x + 1)

Yes, you are correct! The equation you wrote is correct: 8 times the difference between a number (x) and 3 is equal to 6 times the sum of that same number (x) and 1.

To further explain, the equation you provided, 8(x + 3) = 6(x + 1), represents the statement in algebraic form. It consists of two sides, the left side and the right side, separated by an equal sign.

The left side, 8(x + 3), represents "eight times the difference of a number and three." Here, x + 3 represents the difference of the number (x) and 3, and multiplying it by 8 gives us eight times that difference.

The right side, 6(x + 1), represents "six times the sum of a number and one." Similarly, x + 1 represents the sum of the number (x) and 1, and multiplying it by 6 gives us six times that sum.

By setting the left side equal to the right side (8(x + 3) = 6(x + 1)), we express that they are equivalent and represent the same value.

Now, you can go ahead and solve this equation to find the value of x.