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 $$12a + 120 - 8a = 156$$?

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:

$$
4a + 120 = 156
$$

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:

$$
a = rac{36}{4} = 9
$$

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.

Tips for Quickly Solving Similar Equations

• Combine like terms first to reduce complexity.
  
• Always isolate the variable term by undoing addition/subtraction.
  
• Use inverse operations to solve for $a$ (add / subtract to balance, then divide / multiply).
  
• Double-check your answer by substituting $a = 9$ back into the original equation.

Practice Problem

Solve: $$12a + 120 - 8a = 156$$
Can you verify:
$$12(9) + 120 - 8(9) = 156?$$
Yes — $108 + 120 - 72 = 156$ ✔️

Conclusion

Solving $$12a + 120 - 8a = 156$$ is straightforward once you understand the simplification and isolation steps. Use this guide as a template to tackle similar linear equations confidently. Keep practicing — algebra is your gateway to powerful problem-solving skills!

Tags: #Algebra #LinearEquations #MathSolving #AlgebraHelp #ElementaryMath #OnlineMathTutorial #EquationSteps #STEMEducation