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)

if x-1/x = 4, then evaluate x2+1/x2 and x4+1/x4 | Filo

Image Gallery

$1. If $x^2 + 3x + 1 = 0$, then $x + {1}{x} | StudyX$

If x - 1/x = 15/4, then x + 1/x = A. 4 B. 17/4 C. 13/4 D. 1/4 ...

22. If $A - 3X = B$, then $X =$ 1) $ 27 | StudyX

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:

📰 A solution is made by mixing 3 parts water with 2 parts alcohol. If 10 liters of alcohol are used, how many liters of water are needed? 📰 The ratio of water to alcohol is 3:2. 📰 For 2 parts alcohol = 10 liters, 1 part = 5 liters. 📰 Jb Johor 7798037 📰 Unlocking Nano Nuclear Energy The Hidden Breakthrough That Could Power Our Cities 9461050 📰 Download These Ringtones For Iphoneyour Friends Will Be Signs Youre Nailed To Their Phone 1070439 📰 Travel Insured International Reviews 9561019 📰 Shocking Facts About Verona Pharmas Greatest Success Yetyou Wont Believe 7 7217188 📰 Surface Pro 2 In 1 9152556 📰 You Wont Believe How Clicker Heroes Changed The Gaming World Forever 5446809 📰 This Simple Method Got Me The Perfect Brown Paint See The Secret Hack 6636112 📰 You Wont Believe How Much Income Comes In 20 Dollars An Hour 2856632 📰 Click Here To Finally Take Control How To Pull Out Your 401K Fastno More Waiting 2482992 📰 Relaxation Synonym 1389985 📰 Adam And Eve The Boys The Secret Couple Everyones Talking About 5011400 📰 Unlock The Ultimate Your Dictionary Pro Tips No One Tells You 9675603 📰 Hydrogenated Credentials 6313976 📰 Slack App Osx 4569310

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.