Then: -18.5 = x(-22) + (1 - x)(-14)

Solving the Equation: -18.5 = x(-22) + (1 - x)(-14)

Understanding how to solve linear equations is essential in algebra, and tackling expressions like −18.5 = x(−22) + (1 − x)(−14) reveals key techniques that simplify complex formulas into clear, solvable forms. Whether you're a student mastering algebra or a teacher explaining key concepts, this step-by-step guide will help you solve the equation efficiently and boost your problem-solving skills.

Understanding the Context

Step-by-Step Solution to −18.5 = x(−22) + (1 − x)(−14)

Start with the original equation:
−18.5 = x(−22) + (1 − x)(−14)

Step 1: Expand the terms

Multiply out each part:
−18.5 = −22x + (−14) + (1)(−14) − x(−14)
= −22x − 14 − 14 + 14x
(Note: −14×(−x) = +14x)

Key Insights

Combine like terms on the right:
−22x + 14x = −8x
−14 − 14 = −28
So:
−18.5 = −8x − 28

Step 2: Isolate the term with x

Add 28 to both sides:
−18.5 + 28 = −8x − 28 + 28
9.5 = −8x

Step 3: Solve for x

Divide both sides by −8:
x = 9.5 / (−8)
x = −1.1875

🔗 Related Articles You Might Like:

📰 Fed Rate Cut Is Revolutionizing Mortgage Rates—Mortgage Borrowers Are Overreacting! 📰 Mortgage Rates Poised to Plunge After Fed Rate Cut—Heres What You Need to Know Now! 📰 Why the Feds Rate Cut Is Cracking the Mortgage Market—Mortgage Rates Could Drop Overnight! 📰 Ssms Download Windows 📰 Crazy Games Deadshot 📰 How To Combine Names In Excel 4895506 📰 Uncover The Secret Superpowers Of Labratssci Fi Meets Real Science 7922755 📰 Thus F Y Fy So F Is Even 6703400 📰 Watches That Monitor Blood Pressure 5110818 📰 Bankofamerica Portal 📰 How One Simple Haircut Transformed My Whole Looklow Taper Fade Youve Been Dying To Try 5086052 📰 Examples Of Index Funds 📰 Games On Imessage 📰 Bank Of America On Line Banking 📰 Arc Raiders A Lay Of The Land 📰 What Ethnicity Is Bruno Mars 📰 Scp Descent 📰 Hidden Apps Draining Your Iphone This Cleaner Clears Them Instantly 844842

Final Thoughts

Final Answer

x = −1.1875

Why This Equation Matters

Solving equations like −18.5 = x(−22) + (1 − x)(−14) goes beyond algebra homework—it’s foundational for modeling real-world scenarios such as budgeting, proportional reasoning, and physics equations. Mastering this process strengthens logical thinking and prepares you for advanced math topics like systems of equations, quadratic functions, and calculus.

Tips for Solving Similar Equations

Always expand parentheses clearly.
Combine like terms before solving for the variable.
Isolate the variable term step-by-step.
Check your solution by substituting back into the original equation.