Solve Linear Equation: Finding X in -3x+8-11=40x+5x+9

Linear Equations with Multi-Term Simplification

Find the value of the parameter X

3x+811=40x+5x+9 -3x+8-11=40x+5x+9

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to isolate the unknown X
00:07 Let's group terms
00:17 Let's arrange the equation so that one side has only the unknown X
00:33 Let's simplify what we can
00:46 Let's isolate the unknown X and calculate
01:02 Let's simplify what we can
01:06 Let's continue to isolate the unknown X
01:19 Let's factor 48 into 12 and 4
01:25 Let's simplify what we can
01:31 This is the solution to the question

Step-by-step written solution

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1

Understand the problem

Find the value of the parameter X

3x+811=40x+5x+9 -3x+8-11=40x+5x+9

2

Step-by-step solution

To solve the equation 3x+811=40x+5x+9 -3x + 8 - 11 = 40x + 5x + 9 , we need to combine and simplify terms:

  • Simplify each side separately. Start with the right side: 40x+5x+9=45x+9 40x + 5x + 9 = 45x + 9 .
  • Now simplify the left side: 3x+811=3x3 -3x + 8 - 11 = -3x - 3 .

The equation is now: 3x3=45x+9 -3x - 3 = 45x + 9 . Next, move all x x -terms to one side and constants to the other side:

  • Add 3x 3x to both sides: 3x3+3x=45x+9+3x -3x - 3 + 3x = 45x + 9 + 3x , which simplifies to: 3=48x+9 -3 = 48x + 9 .

Then, move the constant term 9 9 to the left side:

  • Subtract 9 9 from both sides: 39=48x+99 -3 - 9 = 48x + 9 - 9 , which simplifies to: 12=48x -12 = 48x .
  • Solve for x x by dividing both sides by 48: x=1248 x = \frac{-12}{48} .
  • Simplify the fraction: x=14 x = -\frac{1}{4} .

Therefore, the solution to the problem is x=14 x = -\frac{1}{4} .

3

Final Answer

14 -\frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • Simplification: Combine like terms on each side before solving
  • Technique: Left side: -3x + 8 - 11 = -3x - 3
  • Check: Substitute -1/4: -3(-1/4) - 3 = 45(-1/4) + 9 gives -12 = -12 ✓

Common Mistakes

Avoid these frequent errors
  • Moving terms without combining like terms first
    Don't jump to moving x-terms across the equals sign before simplifying each side = messy calculations and wrong answers! This creates unnecessary complexity with multiple terms to track. Always combine like terms on each side first, then isolate the variable.

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

Why do I need to combine like terms before solving?

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Combining like terms first makes the equation much simpler! Instead of dealing with 5 terms, you get just 2 terms on each side. This reduces mistakes and makes the solving process clearer.

What's the difference between 40x + 5x and -3x + 8 - 11?

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The first has like terms (both x-terms): 40x + 5x = 45x. The second has unlike terms (x-terms and constants): -3x stays separate, but 8 - 11 = -3.

How do I remember which terms can be combined?

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Only terms with the same variable and same power can combine! So x-terms combine with x-terms, constants combine with constants, but x-terms and constants stay separate.

What if I get a negative fraction as my answer?

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Negative fractions are completely normal! x=14 x = -\frac{1}{4} just means x is negative. Always check by substituting back into the original equation.

Can I solve this equation a different way?

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Yes! You could move terms first, but combining like terms first is usually easier and less error-prone. It's the recommended approach for multi-term equations.

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