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.

Understanding the Context

Step 1: Understanding the Equation
The 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 Variable
Because 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:

\[
x = \frac{-120}{-0.03}
\]

(x, y) \in R \quad \Rightarrow \quad x+4 y=10 \text { but }(y, z) \in R\..

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(x, y) \in R \quad \Rightarrow \quad x+4 y=10 \text { but }(y, z) \in R\..
Let f(x)=y, where x∈R and y∈R \[ \therefore 4 x+3=y \quad \Rightarrow \qu..
Let f(x)=y, where x∈R and y∈R\[\therefore 4 x+3=y \quad \Rightarrow \qu..
\Rightarrow \quad \frac{n !}{(n-1) !}=9 \quad \Rightarrow \quad \frac{n(n..
\[\Rightarrow \quad x=3 \quad\left[x=-\frac{3}{2}(\text { rejected })\ri..

Key Insights

Since dividing two negative numbers results in a positive value, the negatives cancel out, simplifying the calculation.

Step 3: Solving the Division
Now compute:

\[
x = \frac{120}{0.03}
\]

To make the division easier, convert the decimal 0.03 into a fraction:

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A company has a budget of $500,000 for a project. They spend 30% on marketing, 25% on salaries, and 15% on equipment. The remaining budget is allocated to miscellaneous expenses. How much is allocated to miscellaneous expenses?
Total budget: $500,000

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Final Thoughts

\[
0.03 = \frac{3}{100}
\]

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 Answer
The solution to the equation -0.03x = -120 is:

\[
x = \frac{120}{0.03} = 4{,}000
\]

Why This Matters: Real-World Applications
Equations 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.