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:

📰 Why Voodoo Is Labeled a Curse—And Hoodoo’s Secret Survival Trick 📰 You Won’t Believe What Differs Hoodoo From Voodoo Before It Destroys You 📰 The Forbidden Knowledge Battle: Hoodoo vs Voodoo Exposed in This Wild Clash 📰 Greg Brady Exposed The Hidden Truth Youll Wish You Clicked Here Instantly 📰 Greg Bradys Reveal Youve Never Heard Before Dont Miss This 📰 Greg Bradys Shocking Revelation That Will Change Your Life Forever 📰 Greg Eagles Exposed The Shocking Truth Behind His Untold Success 📰 Greg Eagles Hidden Journey From Hiding In Plain Sight To Fame 📰 Greg Heffley Uncovered The Scandal That Kids Are Obsessed With 📰 Greg Heffleys Hidden Struggles Exposedwhy Millions Are Talking About Him 📰 Greg Universe Unveiled The Mind Blowing Secrets You Wont Believe 📰 Gregor Clegane Secrets Revealed The Faceless Monster Behind Bran The Broken 📰 Gregor Clegane Unleashed The True Face Of The Mad King In Westeros 📰 Gregor Samsas Nightmare Revealed Why His Transformation Still Haunts Readers 📰 Gregor Samsas Proper Transformation Revealed The Shocking Secret That Changed Everything 📰 Gregory Greg Heffley Revealed The Hidden Truth Behind The Famous Diary Of A Wimpy Kid Mom 📰 Gregory Greg Heffleys Shocking Secrets That Will Change How You See Family Drama Forever 📰 Gregory Horror Show Exposed The Scariest Secrets Behind His Rise To Cult Fame

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.