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
00:08 Let's solve the problem!
00:11 First, we need to isolate the unknown, X.
00:15 Let's group similar terms together.
00:25 Now, arrange the equation so only X is on one side.
00:41 Next, simplify the equation where possible.
00:54 Let's isolate X and do the calculation.
01:10 Simplify again if needed.
01:14 Keep working to isolate X.
01:27 Factor forty-eight into twelve and four.
01:33 Simplify one more time.
01:39 And that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
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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