Solve for X: Simplifying x+3-4x=5x+6-1-8x Step by Step

Linear Equations with No Solution

Solve for X:

x+34x=5x+618x x+3-4x=5x+6-1-8x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:03 Collect terms
00:21 Isolate the unknown X
00:34 Reduce wherever possible
00:38 All the unknowns cancel each other out therefore there is no solution to the question
00:44 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

x+34x=5x+618x x+3-4x=5x+6-1-8x

2

Step-by-step solution

To solve the given problem, we'll proceed as follows:

  • Step 1: Simplify both sides of the equation.
  • Step 2: Check if x x can be isolated or analyze if the equation results in contradictions.

Now, let's work through each step:
Step 1: Simplify the left side: x+34x=(1x4x)+3=3x+3 x + 3 - 4x = (1x - 4x) + 3 = -3x + 3 .
Step 2: Simplify the right side: 5x+618x=(5x8x)+(61)=3x+5 5x + 6 - 1 - 8x = (5x - 8x) + (6 - 1) = -3x + 5 .

The simplified equation becomes:

3x+3=3x+5-3x + 3 = -3x + 5

To solve for x x , we attempt to isolate x x . If we add 3x 3x to both sides to eliminate the 3x-3x terms, we get:

3=53 = 5

This results in a contradiction, as 3 is not equal to 5, indicating that there is no value of x x that can satisfy this equation.

Therefore, the solution to the problem is no solution as indicated by the contradiction.

3

Final Answer

No solution

Key Points to Remember

Essential concepts to master this topic
  • Simplification Rule: Combine like terms on each side separately first
  • Technique: When 3x+3=3x+5 -3x + 3 = -3x + 5 , add 3x to eliminate variables
  • Check: If constants remain unequal (3 ≠ 5), no solution exists ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the equation always has a solution
    Don't keep trying to solve when you get 3 = 5 after eliminating variables! This contradiction means no x-value works. Always recognize that when identical variable terms cancel but constants don't match, there's no solution.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

What does 'no solution' actually mean?

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It means no number can replace x to make the equation true. When you simplify and get something impossible like 3 = 5, the original equation has no solution.

How is this different from x = 0?

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Very different! When x = 0, zero is the solution. 'No solution' means not even zero works - no number at all can satisfy the equation.

Can I still check my work if there's no solution?

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Yes! Verify by substituting any number for x in the original equation. You'll see that the left and right sides never equal each other, confirming no solution.

What if I made an algebra mistake instead?

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Double-check your combining of like terms! Make sure you have 3x+3=3x+5 -3x + 3 = -3x + 5 . If your simplification is correct and you get a false statement, then no solution is right.

Do all linear equations have solutions?

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No! Linear equations can have:

  • One solution (most common)
  • No solution (like this problem)
  • Infinite solutions (when both sides are identical)

How do I write 'no solution' on my homework?

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You can write: 'No solution', '∅' (empty set symbol), or 'The equation has no solution'. All are correct ways to express this!

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