Solve the Linear Equation: 800-2x-x=803 Step by Step

Q: Why do I combine -2x and -x first instead of moving terms around?

Combining like terms simplifies the equation before you start moving things around. It's much easier to work with $ 800 - 3x = 803 $ than the original messy equation!

Q: Why is my answer negative when the numbers in the problem are positive?

That's totally normal! The equation $ 800 - 3x = 803 $ means we need to subtract more from 800 to get 803. Since 803 > 800, x must be negative.

Q: Can I check my answer a different way?

Yes! You can also rearrange to $ 800 - 803 = 2x + x $, which gives $ -3 = 3x $, so $ x = -1 $. Same answer!

Q: What if I accidentally wrote 800 + 2x + x = 803?

Double-check the original problem! Signs are super important. The problem shows $ 800 - 2x - x $, which means both x terms are being subtracted.

Linear Equations with Like Term Combination

$800-2x-x=803$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's solve this equation.

00:08 Our goal is to find the value of X.

00:12 We'll rearrange the equation so that X is on one side by itself.

00:29 Great job! X is now isolated.

00:34 And that's how we find the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$800-2x-x=803$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Combine like terms on the left side of the equation.
Step 2: Isolate the variable $x$ on one side of the equation.
Step 3: Solve for $x$ and simplify the result.

Now, let's work through each step:
Step 1: The left side of the equation is $800 - 2x - x$ . Combine the terms with $x$ :
This becomes $800 - 3x = 803$ .

Step 2: Subtract 800 from both sides to isolate the term with $x$ :
$800 - 3x - 800 = 803 - 800$
This simplifies to $-3x = 3$ .

Step 3: Divide both sides by -3 to solve for $x$ :
$x = \frac{3}{-3}$
Thus, $x = -1$ .

Therefore, the solution to the problem is $x = -1$ .

Final Answer

$x=-1$

Key Points to Remember

Essential concepts to master this topic

Combining Terms: Add coefficients of like terms: $-2x - x = -3x$
Technique: Isolate variable by subtracting 800: $800 - 3x = 803$ becomes $-3x = 3$
Check: Substitute $x = -1$ back: $800 - 2(-1) - (-1) = 803$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms before solving
Don't solve 800 - 2x - x = 803 by moving terms around without combining first = messy algebra and wrong answers! This creates confusion with multiple x terms scattered throughout. Always combine like terms (-2x - x = -3x) as your very first step.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I combine -2x and -x first instead of moving terms around?

Combining like terms simplifies the equation before you start moving things around. It's much easier to work with $800 - 3x = 803$ than the original messy equation!

How do I know -2x - x equals -3x?

Think of it like this: if you owe 2 dollars and then owe 1 more dollar, you owe 3 dollars total. So $-2x - x = -3x$ .

Why is my answer negative when the numbers in the problem are positive?

That's totally normal! The equation $800 - 3x = 803$ means we need to subtract more from 800 to get 803. Since 803 > 800, x must be negative.

Can I check my answer a different way?

Yes! You can also rearrange to $800 - 803 = 2x + x$ , which gives $-3 = 3x$ , so $x = -1$ . Same answer!

What if I accidentally wrote 800 + 2x + x = 803?

Double-check the original problem! Signs are super important. The problem shows $800 - 2x - x$ , which means both x terms are being subtracted.

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