Simplify: $ 5x + 6 = 102 $. - Coaching Toolbox
Simplify $ 5x + 6 = 102 $: A Step-by-Step Guide to Solving Linear Equations
Simplify $ 5x + 6 = 102 $: A Step-by-Step Guide to Solving Linear Equations
Solving algebraic equations is a fundamental skill in math, and simplifying expressions like $ 5x + 6 = 102 $ is essential for students, educators, and lifelong learners alike. Whether you're tackling this equation for homework, preparing for a math test, or building foundational knowledge, understanding how to isolate the variable and solve it step by step is key. In this article, we break down how to simplify and solve the equation $ 5x + 6 = 102 $ clearly and precisely.
Understanding the Context
What Is the Equation $ 5x + 6 = 102 $?
The equation $ 5x + 6 = 102 $ is a linear equation in one variable, where $ x $ represents an unknown number. The goal is to find the value of $ x $ that makes the equation true.
Step 1: Subtract 6 from Both Sides
To isolate the term with $ x $, begin by eliminating the constant on the left side. Subtract 6 from both sides:
$$
5x + 6 - 6 = 102 - 6
$$
Simplify:
$$
5x = 96
$$
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Key Insights
This step uses the principle of equality — whatever you do to one side, you do to the other to maintain balance.
Step 2: Divide Both Sides by 5
Now, divide both sides by 5 to solve for $ x $:
$$
rac{5x}{5} = rac{96}{5}
$$
Simplify:
$$
x = 19.2
$$
Since 96 divided by 5 equals 19.2, the solution is $ x = 19.2 $.
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Why Simplifying $ 5x + 6 = 102 $ Matters
Mastering this simple linear equation helps build confidence in algebra. The process involves:
- Isolating variables: Moving constants to the opposite side using addition/subtraction.
- Balancing equations: Performing identical operations on both sides to preserve equality.
- Inverting operations: Using division to undo multiplication.
These fundamental skills apply not just to math homework, but also to real-world problems involving budgeting, planning, and data analysis.
Final Answer
$$
oxed{x = 19.2}
$$
Additional Tips for Simplifying Linear Equations
- Always simplify expressions fully before solving.
- Use inverse operations in the correct order: start by undoing addition with subtraction, then multiplication with division.
- Check your solution by substituting $ x = 19.2 $ back into the original equation:
$$
5(19.2) + 6 = 96 + 6 = 102
$$
The equation holds true, confirming your answer is correct.
