Simplify: $2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15$.

Simplify: How to Solve the Equation $2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15$ Step-by-Step

Solving equations is a fundamental skill in algebra, and simplifying complex expressions often makes the process clearer and easier. One common equation students encounter is:

$$
2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15
$$

Understanding the Context

At first glance, this looks daunting, but with careful step-by-step simplification, you can solve for $ t $ efficiently. This article breaks down how to simplify the left-hand side, combine like terms, isolate the variable, and solve the equation.

Step 1: Combine Like Terms on the Left Side

The left side of the equation is:

Key Insights

$$
2t + 1 - t + 4 + 3t - 2
$$

Group all the terms involving $ t $ and constant terms:

Combine $ t $-terms: $ 2t - t + 3t = (2 - 1 + 3)t = 4t $
Combine constant terms: $ 1 + 4 - 2 = 3 $

So, the left-hand side simplifies to:

$$
4t + 3
$$

🔗 Related Articles You Might Like:

📰 So all edges are of length $\sqrt{2}$. 📰 Let’s find $(x, y, z)$ such that its distance to each of the three points is also $\sqrt{2}$: 📰 Distance from $(0,0,0)$: 📰 Step Into Tryndamere Unlock The Ultimate Build For Epic World Building Magic 📰 Step Outside Trenzas Para Hombres That Make Every Look Instantly Confident 📰 Step Up Your Beach Game Triangle Bikini Secrets You Need To Try Today 📰 Step Up Your Home Decor With A Sleek Tv Cabinet That Hides Your Tv Like Magic Click To See Designs That Wow 📰 Step Up Your Outfit Game The Tweed Jacket Thats Got Everyone Talking Unbelievably Stylish 📰 Step Up Your Style With These Perfect Trucker Hats For Womenlook Cash Carrying 📰 Still Burnin Top Twisted Metal Season 2 Cast Members Uncoveredgot Your Moment Of Madness 📰 Stock Market Alert Can Turkey Stock Crash Or Conquer Find Out Before Its Too Late 📰 Stop Boring Your Yard Discover The Stunning Tree Ornamental Designer Plants Making Waves 📰 Stop Confusing Hair Types Heres The Ultimate List You Cant Ignore 📰 Stop Dropping Tissue Disastersthis Organic Tissue Box Cover Wipes It Off 📰 Stop Drowning In Debthow Traceloanscom Debt Consolidation Transformed 10000 Lives 📰 Stop Dumping Trash Try Trashbytes And Transform Your Waste Game 📰 Stop Enemies Fast With Td 4 Ultra Efficient Tower Defense Gameplay 📰 Stop Feeding The Landfill This Trash Faction Is Changing Everythingfor Good

Final Thoughts

Thus, the equation becomes:

$$
4t + 3 = 15
$$

Step 2: Isolate the Variable Term

Now, subtract 3 from both sides to eliminate the constant:

$$
4t + 3 - 3 = 15 - 3
$$
$$
4t = 12
$$

Step 3: Solve for $ t $

Divide both sides by 4:

$$
t = rac{12}{4} = 3
$$