-0.03x = -120 \quad \Rightarrow \quad x = \frac{120}{0.03} = 4,000
Solving the Equation: -0.03x = -120 – A Step-by-Step Guide
When tackling math problems like linear equations, simplification and clarity are key. One common equation students encounter is -0.03x = -120. Solving this equation not only strengthens algebraic skills but also demonstrates the power of basic math operations in real-world applications. In this article, we’ll walk through how to solve -0.03x = -120, showing every step from rearranging the equation to finding the exact value of x.
Step 1: Understanding the EquationThe equation -0.03x = -120 means that negative zero point zero three multiplied by an unknown value x equals negative one twenty. Our goal is to isolate x and determine its numerical value.
Step 2: Isolating the VariableBecause x is multiplied by -0.03, we use division (the reverse operation of multiplication) to isolate x. This means dividing both sides of the equation by -0.03:
\[x = \frac{-120}{-0.03}\]
Since dividing two negative numbers results in a positive value, the negatives cancel out, simplifying the calculation.
Step 3: Solving the DivisionNow compute:
\[x = \frac{120}{0.03}\]
To make the division easier, convert the decimal 0.03 into a fraction:
\[0.03 = \frac{3}{100}\]
Thus,
\[x = 120 \div \frac{3}{100} = 120 \ imes \frac{100}{3}\]
Simplify:
\[x = 120 \ imes \frac{100}{3} = \frac{12000}{3} = 4000\]
Step 4: Final AnswerThe solution to the equation -0.03x = -120 is:
\[x = \frac{120}{0.03} = 4{,}000\]
Why This Matters: Real-World ApplicationsEquations like -0.03x = -120 appear frequently in finance, science, and engineering. For example:- Finance: Calculating interest rates or depreciation over time.- Physics: Determining rates of change or motion when negative values indicate reversal or decay.- Data Analysis: Finding proportional relationships in scaled datasets.
Mastering these basic algebraic steps builds a solid foundation for advanced problem-solving.
Summary- Start with -0.03x = -120.- Divide both sides by -0.03 (or convert to fraction form).- Simplify: x = 120 ÷ 0.03 = 4,000.- The solution: x = 4{,}000.
了解如何解 Linear Equations 是提升数学素养的关键技能，掌握这种基本变换助于解决复杂问题，拓展思维应用。
Discover more math tutorials and problem-solving tips on our website — because every equation has a story waiting to be understood.
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