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:
$$
5x = 96
$$

Solved: Simplify. * (5x-2)^2 [algebra]

Image Gallery

Solved: Simplify. * (5x-2)^2 [algebra]
Solved: Fully simplify 5x^2/11x [Math]
Solved Simplify: x^2 + 5x + 6/x^3 + 3x^2 - 4x - 12 | Chegg.com
Solved Simplify.5x-6(x-5y) | Chegg.com
Solved Remove parentheses and simplify.5x+6x-(8x+10) | Chegg.com

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 $.

Continue Reading

But the instruction is to generate one. So we instead replace the last question with a corrected, solvable version:
No solution for zero cross product either.
But cross product zero only if parallel, which would require:

🔗 Related Articles You Might Like:

📰 Why PEMIF Stock Is About to Surpass $100—Heres the Shocking Reason! 📰 Shocked Investors: PEMIF Stock Hides a Secret That Could Change Investing Forever! 📰 Dont Miss Out—PEMIF Stock Is Surging Fast, and Experts Say Its Just Getting Started! 📰 Bandana Waddle Dee The Hidden Trend Making Heads Turn Shop Now 1437050 📰 Nvcr Stock Breakout Strategy Why This Surprising Trade Quietly Grows Fast 5989755 📰 Guntouchable 1201583 📰 Ktlo Possesses Power No One Knows You Usediscover The Secret Now 5895444 📰 Pepperoni For Dogs Dog Watchers Are Obsessedheres The Surprising Truth 5312583 📰 Access Your Merrick Bank Credit Card Nowbut Be Careful What You See 616768 📰 Boost Your Returns Fidelity Investments Madison Wi Leads The Way In Smart Wealth Growth 8458134 📰 Ghost Bat You Wont Believe Lives In Your Atticthis Shadow Is Rising Again 2261551 📰 Master Chic Knit Designsturn Heads With These Easy To Follow Patterns 92797 📰 Best Home Water Softener 4745983 📰 Kang Han Na Movies 1188562 📰 Foamposite Betrayal Revealedis It Actually Worth It 1855140 📰 Why Every Student Needs Fidelitys Unique 4565932 📰 Sql Query Switch Case 6441707 📰 G El Control Oculomotor 8365255

Final Thoughts

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.