Solve $ (9a + b) - (6a + b) = -9 - 5 $: A Step-by-Step Breakdown

In algebra, solving equations step-by-step not only reinforces mathematical concepts but also builds problem-solving confidence. Today, we’ll solve the equation:

$$
(9a + b) - (6a + b) = -9 - 5
$$
and derive that $ a = - rac{14}{3} $. This article walks you through each logical step to clearly understand how to isolate the variable $ a $ and find its exact value.

Understanding the Context

Step 1: Simplify Both Sides

Start by simplifying the expressions on both sides of the equation.

  • The left-hand side:
    $(9a + b) - (6a + b)$
    Distribute the negative sign:
    $9a + b - 6a - b$
$ (9a + b) - (6a + b) = -9 - 5 \Rightarrow 3a = -14 \Rightarrow a = -\frac{14}{3} $

Key Insights

  • The right-hand side:
    $-9 - 5 = -14$

Now the equation becomes:
$$
9a + b - 6a - b = -14
$$

Step 2: Combine Like Terms

Combine like terms on the left side:
$ (9a - 6a) + (b - b) = 3a + 0 = 3a $

Continue Reading

2000 ford mustang gt
2000 gmc sierra
2000 jeep cherokee

🔗 Related Articles You Might Like:

📰 The Silence After the Gunfire Reveals a Story No One Spoke About 📰 Shocking Truth Behind the Colorado Shooting That Shook a Whole Nation 📰 Cocodona 250 Secrets No One Talks About But Everyone Swears By 📰 Helsing Tv Unleashed You Wont Believe What This Must Watch Show Delivers 📰 Helter Skelter Helter Skelter The Hidden Terror You Didnt Know You Needed 📰 Hem Dress Pants Sewing Machine Hack Perfect Fit In Minutes 📰 Heman Exposed The Ultimate Truth This Rivals Downfall Was Unavoidable 📰 Heman Stunned Us Allwhat This Champion Revealed Will Blow Your Mind 📰 Hemosiderin Staining Explained The Shocking Truth About Iron Accumulation In Tissues 📰 Hemosiderin Staining The Secret Superpower Of Detecting Iron Depositsheres Why Its Essential 📰 Hen Coop Finally Escapes Relive The Chaos Of The Big Run 📰 Henai Streaming Exposed The Extreme Content Youve Been Warning Us About 📰 Henchmen Exposed How These Loyal Saboteurs Are Fueling Corporate Empires 📰 Henchmen Unleashed The Ultimate Secret Army Behind Every Influence Driven Business 📰 Hendrickson Toyota Coconut Creek Florida Reveals Secret Deal Dont Miss This Game Changing Offer 📰 Hendrickson Toyota In Coconut Creek Just Unveiled The Most Exclusive Toy Collection Find Out Why 📰 Henetati Teens Exposed Everything You Never Knew About Their Hidden World Click To Discover 📰 Henetati Teens Secrets The Untold Story Thats Making Teens Nationwide Talk

Final Thoughts

So the equation simplifies to:
$$
3a = -14
$$

Step 3: Solve for $ a $

Divide both sides by 3:
$$
a = - rac{14}{3}
$$

Why $ b $ Cancel Out

Notice that $ b $ appears on both sides of the original equation: once inside the first parentheses as $ +b $, and again negatively as $ -b $. When simplified, $ +b - b = 0 $, effectively removing $ b $ from the equation. This highlights a crucial algebraic insight—terms that appear with opposite signs can cancel when simplifying.

Final Answer

$$
a = - rac{14}{3}
$$