the sum of 4 times a number and -2 is equal to the sum of 5 times the number and -2. find the number.

translate into math ....

4x - 2 = 5x - 2

now solve it.

You should have seen the obvious answer by the "just think about it" theorem.

Let's represent the unknown number as "x".

The sum of 4 times the number and -2 can be written as 4x - 2.
The sum of 5 times the number and -2 can be written as 5x - 2.

According to the given problem, we have the equation:

4x - 2 = 5x - 2

To find the value of "x", we can start by isolating the variable terms on one side of the equation.

Subtracting 4x from both sides:

4x - 4x - 2 = 5x - 4x - 2
-2 = x - 2

Now, adding 2 to both sides:

-2 + 2 = x - 2 + 2
0 = x

Therefore, the number is 0.

To solve this problem, we'll use algebraic equations. Let's start by assigning a variable to the unknown number. Let's call the number "x".

According to the problem, the sum of 4 times the number and -2 is equal to the sum of 5 times the number and -2. We can express this as the following equation:

4x - 2 = 5x - 2

Now, we'll simplify the equation by combining like terms. Notice that both sides of the equation have a -2, so we can cancel them out:

4x = 5x

Next, we'll move all the terms with "x" to one side of the equation. We can do this by subtracting 4x from both sides:

4x - 4x = 5x - 4x
0 = x

Now we have x = 0. This means the unknown number is 0.