Final answer:
The equation describing the given situation is 2(x + 20) = 5x - 2. After simplifying, we find that x equals 14.
Step-by-step explanation:
To find the equation that represents the situation where a number is first increased by 20, then doubled, and the result is 2 less than 5 times the number, we need to translate the words into a mathematical equation. Let's let 'x' represent the unknown number. According to the problem, the number is first increased by 20, so we have x + 20. Then, this result is doubled, which gives us 2(x + 20). Finally, we are told that this doubled amount is 2 less than 5 times the original number, meaning the equation can be written as:
2(x + 20) = 5x - 2
To solve the equation, we distribute the 2 on the left side:
2x + 40 = 5x - 2
Then, we move all terms involving x to one side and constants to the other:
2x - 5x = -2 - 40
-3x = -42
Lastly, divide both sides by -3 to get the value of x:
x = 14