Four times a number, diminished by 6, yields the same result as twice the same number increased by 4. Find the number.
just translate the English into Math,
4x - 6 = 2x + 4
then solve for x
4 n - 6 = 2 n + 4
2 n = 10
n =5
4x-6=2x+4
To solve this equation, let's assign a variable to the unknown number. Let's call the number "x".
According to the problem, "Four times a number, diminished by 6, yields the same result as twice the same number increased by 4." We can translate this into the following equation:
4x - 6 = 2x + 4
To find the value of x, let's isolate the variable on one side of the equation. We can do this by performing algebraic operations:
4x - 2x = 4 + 6
2x = 10
Now, divide both sides of the equation by 2 to solve for x:
x = 10/2
Simplifying the expression, we find:
x = 5
Therefore, the number is 5.