$$ 12a + 120 - 8a = 156 $$ - Decision Point
How to Solve the Linear Equation $$ 12a + 120 - 8a = 156 $$ – A Step-by-Step Guide with Practical Insights
How to Solve the Linear Equation $$ 12a + 120 - 8a = 156 $$ – A Step-by-Step Guide with Practical Insights
Understanding how to solve linear equations is a foundational skill in algebra, but mastering it opens doors to advanced math and real-world problem solving. One commonly encountered equation is $$12a + 120 - 8a = 156$$. This article breaks down the step-by-step solution process, explains key algebraic concepts, and offers practical insights to strengthen your math fundamentals.
What Is the Equation $$12a + 120 - 8a = 156$$?
Understanding the Context
The given equation is a linear equation in one variable, $a$. Simplifying it helps isolate $a$ on one side, making it easier to solve. This type of equation frequently appears in math assessments, standardized tests, and real-life scenarios involving budgets, rates, and measurements.
Step-by-Step Solution
Step 1: Simplify the Left-Side Expression
Combine like terms on the left-hand side. Note that $12a - 8a = 4a$, so the equation simplifies to:
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Key Insights
$$
4a + 120 = 156
$$
Step 2: Isolate the Variable Term
Subtract 120 from both sides to move the constant to the right:
$$
4a = 156 - 120 = 36
$$
Step 3: Solve for $a$
Now divide both sides by 4:
$$
a = rac{36}{4} = 9
$$
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Final Answer
The solution to the equation $$12a + 120 - 8a = 156$$ is:
$$
oxed{a = 9}
$$
Why Solving Linear Equations Matters
Linear equations like $$12a + 120 - 8a = 156$$ are more than abstract math — they model everyday situations such as:
- Calculating total cost after discounts
- Budgeting monthly expenses
- Determining time or distance travel
Mastering these equations builds logical reasoning and analytical skills essential for STEM fields, finance, engineering, and data science.
