Solve Linear Equation: 2-5x+4-1x=0 with Like Terms

Linear Equations with Combining Like Terms

25x+41x=0 2-5x+4-1x=0

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Step-by-step video solution

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00:00 Solve
00:04 Collect terms
00:08 We want to isolate the unknown X
00:12 Let's arrange the equation so that one side has only the unknown X
00:28 We'll isolate the unknown X, and calculate
00:39 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

25x+41x=0 2-5x+4-1x=0

2

Step-by-step solution

To solve the equation 25x+41x=0 2 - 5x + 4 - 1x = 0 , we proceed as follows:

  • Step 1: Simplify the left side of the equation.

Combine the constant terms 22 and 44:

2+4=6 2 + 4 = 6

Combine the terms involving x x :

5x1x=6x-5x - 1x = -6x

Thus, the equation becomes:

66x=0 6 - 6x = 0

  • Step 2: Isolate the variable x x .

Move 66 to the other side of the equation by subtracting 66 from both sides:

6x=6 -6x = -6

Divide both sides by 6-6 to solve for x x :

x=66=1 x = \frac{-6}{-6} = 1

Therefore, the solution to the equation is x=1 x = 1 .

3

Final Answer

x=1 x=1

Key Points to Remember

Essential concepts to master this topic
  • Combining: Group constants together and x-terms together separately
  • Technique: 2 + 4 = 6 and -5x + (-1x) = -6x
  • Check: Substitute x = 1: 2 - 5(1) + 4 - 1(1) = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Not combining like terms correctly
    Don't combine constants with x-terms or ignore negative signs = wrong simplification! This creates equations that can't be solved properly. Always group constants separately from variables and pay careful attention to positive and negative signs.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

What are 'like terms' exactly?

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Like terms have the same variable with the same power. In this problem, 2 and 4 are like terms (both constants), and -5x and -1x are like terms (both have x to the first power).

Why do I combine like terms first instead of moving terms around?

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Combining like terms simplifies the equation and makes it easier to solve! It's much cleaner to work with 66x=0 6 - 6x = 0 than the original messy equation.

How do I handle the negative signs when combining?

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Treat negative signs as part of the term! So -5x - 1x becomes (-5) + (-1) = -6, giving you 6x -6x . Always be careful with your signs!

What if I get a different arrangement of terms?

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The order doesn't matter when combining! Whether you write 2+45x1x=0 2 + 4 - 5x - 1x = 0 or 5x1x+2+4=0 -5x - 1x + 2 + 4 = 0 , you'll get the same simplified result.

Can I solve without combining like terms?

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Technically yes, but it's much harder! You'd have to move each term one at a time. Combining like terms first makes the algebra cleaner and reduces chances for errors.

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