Translate the sentence “The difference of x and 0.1 is -4.82 .” into an algebraic equation and then solve.
The Correct Answer and Explanation is:
Algebraic Equation:
The sentence “The difference of x and 0.1 is -4.82” can be written as:x−0.1=−4.82x – 0.1 = -4.82x−0.1=−4.82
Solution:
To find the value of xxx, we need to isolate xxx on one side of the equation. The equation is:x−0.1=−4.82x – 0.1 = -4.82x−0.1=−4.82
To eliminate the −0.1-0.1−0.1 on the left-hand side, we add 0.1 to both sides of the equation:x−0.1+0.1=−4.82+0.1x – 0.1 + 0.1 = -4.82 + 0.1x−0.1+0.1=−4.82+0.1x=−4.72x = -4.72x=−4.72
Final Answer:x=−4.72x = -4.72x=−4.72
Explanation:
This problem involves translating a verbal sentence into a mathematical equation and then solving for an unknown. The sentence given is “The difference of x and 0.1 is -4.82.” The word “difference” refers to subtraction. So the phrase “the difference of x and 0.1” means we subtract 0.1 from x, or mathematically, x−0.1x – 0.1x−0.1. The phrase “is -4.82” indicates that this expression is equal to -4.82. Putting this all together, we get the equation:x−0.1=−4.82x – 0.1 = -4.82x−0.1=−4.82
To solve for xxx, we perform the inverse operation of subtraction, which is addition. We add 0.1 to both sides of the equation. This step is important because it helps isolate the variable xxx, which is what we are solving for. When we add 0.1 to both sides, we maintain the balance of the equation.
So the left side becomes xxx (since −0.1+0.1=0-0.1 + 0.1 = 0−0.1+0.1=0), and the right side becomes −4.82+0.1=−4.72-4.82 + 0.1 = -4.72−4.82+0.1=−4.72.
Therefore, the solution is:x=−4.72x = -4.72x=−4.72
This means that if you subtract 0.1 from -4.72, you will get -4.82, which confirms the correctness of the solution. This is a typical one-step equation and is a basic but essential concept in algebra.
