What is the Solution to the Linear Equation? D – 10 – 2d + 7 = 8 + D – 10 – 3d
When you first look at a linear equation like this — What is the Solution to the Linear Equation? D – 10 – 2d + 7 = 8 + D – 10 – 3d — it might seem overwhelming, especially if you’re not a math lover. But don’t worry! Today, we’re going to walk through this equation slowly and clearly. You don’t need to be a math whiz to understand it. Whether you’re a student brushing up on algebra, a parent helping with homework, or just someone curious about solving equations, you’re in the right place.
First Things First: What Is a Linear Equation?
Before diving into this specific equation, let’s break down what a linear equation actually is. A linear equation is just a math sentence that shows that two things are equal. Typically, it involves variables like “x” or “d”, numbers, and arithmetic operations such as addition, subtraction, and multiplication.
Here’s an easy way to think of it: a linear equation is like a balancing scale. Whatever you do on one side, you need to do the same on the other to keep it even. That’s the golden rule.
Step 1: Take a Good Look at the Equation
Let’s write down the problem we’re trying to solve so we can see it clearly:
D – 10 – 2d + 7 = 8 + D – 10 – 3d
At first glance, it’s a bit messy. There are variables and numbers all over the place. But don’t let that intimidate you. All we need is a little organization and some basic rules of algebra.
Step 2: Combine Like Terms
This step is kind of like tidying your room—you group similar things together. In this case, we’re grouping like terms, which just means terms that have the same variable or are constants (numbers without variables).
Let’s do this first on the left-hand side:
– D – 2d is just combining the variable terms. D is the same as 1d, so:
1d – 2d = -1d
– The constants: -10 + 7 = -3
So the left-hand side becomes:
-1d – 3
Now for the right-hand side:
– D – 3d = -2d
– 8 – 10 = -2
So the right-hand side becomes:
-2d – 2
Now our equation looks much simpler:
-1d – 3 = -2d – 2
Looking better already, right?
Step 3: Get the Variables on One Side
Just like doing laundry—shirts in one basket, socks in another—we want to get all our variable terms on one side and constants on the other.
Let’s move the -2d from the right side to the left. To do that, we’ll add 2d to both sides:
-1d + 2d –3 = -2d + 2d – 2
Simplify both sides:
– Left: -1d + 2d = 1d → so we have d – 3
– Right: -2d + 2d = 0 → so we have just -2
Now the equation is:
d – 3 = -2
Nice! Now we’re almost there.
Step 4: Solve for the Variable
We want to find out what value of d makes both sides equal. So let’s isolate d by getting rid of the -3 on the left. We do this by adding 3 to both sides:
d – 3 + 3 = -2 + 3
This simplifies to:
d = 1
That’s it! You’ve just solved it. The solution to the equation What is the Solution to the Linear Equation? D – 10 – 2d + 7 = 8 + D – 10 – 3d is:
d = 1
Double-Checking Your Work
It’s always a smart move to check your work. Let’s plug d = 1 back into the original equation and see if both sides are equal.
Starting with the left-hand side:
D – 10 – 2d + 7
= 1 – 10 – 2(1) + 7
= 1 –10 –2 +7
= -4
Now the right-hand side:
8 + D – 10 – 3d
= 8 + 1 –10 – 3(1)
= 8 +1 –10 –3
= -4
Both sides are equal to -4, so we’re good! It checks out.
Why It Matters
You might be wondering: “Why should I care about solving linear equations?” Well, beyond helping you pass math class, equations like this pop up in real life more often than you’d expect.
Think about this:
These scenarios often rely on understanding relationships between numbers — exactly what equations are all about.
Tips for Solving Similar Linear Equations
Let’s make things a bit easier going forward. Here are some handy tips you can use whenever you’re solving equations like What is the Solution to the Linear Equation? D – 10 – 2d + 7 = 8 + D – 10 – 3d:
Still Feeling Stuck? You’re Not Alone
Sometimes, even when we try our best, math can be frustrating. I remember struggling with equations in high school. I’d stare at a problem for ages without knowing what to do next. What helped me was breaking it down — just like we did today — and asking “What’s the next simple thing I can do?”
And of course, leaning on helpful resources is a game-changer. If you’re a visual learner, drawing things out really helps. If you’re interested in learning more about how variables work, check out this post on Understanding Variables in Algebra — it’s a great stepping stone.
Practice Makes Progress
Let’s challenge you a little. Try solving this one on your own using the steps we discussed.
2x – 5 + 3 = 1 + x – 2
What’s x? (Hint: Start by combining like terms!) Give it a shot, and see if you can simplify both sides, then isolate the variable.
Final Thoughts
Solving a problem like What is the Solution to the Linear Equation? D – 10 – 2d + 7 = 8 + D – 10 – 3d might seem scary at first. But once you take it step-by-step, it becomes a simple and even satisfying puzzle to crack. It’s just about keeping things balanced, simplifying piece by piece, and not giving up.
With time, solving linear equations can feel as natural as tying your shoes. The more you unpack how they work, the more confident you’ll get.
So next time you’re faced with a tricky-looking equation, remember: You’ve got this. Just break it down, keep it balanced, and take one small step at a time.
And hey, even if you forget what to do, this guide will be here to help. Nothing’s impossible with a little patience and practice.
Happy solving!