The difference between 5 times a number and 12 is -27 . Write an equation for this situation and use it to find the number.
The correct answer and explanation is:
To translate the word problem into an equation, let the unknown number be represented by x. The phrase “5 times a number” can be written as 5x. The problem states that the difference between 5 times the number and 12 is -27. This means we subtract 12 from 5 times the number, which gives us 5x – 12. According to the problem, this expression equals -27. So the equation is: 5x−12=−275x – 12 = -27
To solve for x, follow these steps:
- Add 12 to both sides of the equation to eliminate the -12 on the left-hand side: 5x−12+12=−27+125x – 12 + 12 = -27 + 12 Simplifying this: 5x=−155x = -15
- Divide both sides of the equation by 5 to isolate x: 5×5=−155\frac{5x}{5} = \frac{-15}{5} Simplifying this: x=−3x = -3
Thus, the number is -3.
Explanation:
This equation represents the relationship between a number and the operations described in the word problem. First, translating the phrases into algebraic expressions is key. By following the logical steps of isolating x, we arrive at the solution. This kind of problem involves basic algebraic manipulation—first isolating terms, then performing arithmetic operations to solve for the unknown. Understanding these steps is essential for solving similar algebraic equations in the future.