Solve for X in -3x+8=7x-12: Linear Equation Solution

Linear Equations with Variable Terms

Solve for X:

−3x+8=7x−12 -3x+8=7x-12

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve the problem together.
00:10 First, we need to focus on getting X by itself.
00:29 Let's simplify what we can to make it easier.
00:42 Now, keep working to free X from the equation.
01:05 Simplifying again will help us a lot.
01:10 Almost there! Let's get X completely alone.
01:20 And there we have it, the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

−3x+8=7x−12 -3x+8=7x-12

2

Step-by-step solution

We will solve the equation step by step:

Given equation:
−3x+8=7x−12 -3x + 8 = 7x - 12

  • Step 1: Move all x x -terms to one side by adding 3x 3x to both sides.
    −3x+3x+8=7x+3x−12 -3x + 3x + 8 = 7x + 3x - 12
    This simplifies to:
    8=10x−12 8 = 10x - 12
  • Step 2: Move constant terms to the opposite side by adding 12 12 to both sides.
    8+12=10x−12+12 8 + 12 = 10x - 12 + 12
    Which simplifies to:
    20=10x 20 = 10x
  • Step 3: Solve for x x by dividing both sides by 10 10 .
    2010=10x10 \frac{20}{10} = \frac{10x}{10}
    This gives us:
    x=2 x = 2

Therefore, the solution to the equation is x=2 x = 2 .

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Collect all x-terms on one side, constants on other
  • Technique: Add 3x to both sides: 8 = 10x - 12
  • Check: Substitute x = 2: -3(2) + 8 = 7(2) - 12 → 2 = 2 ✓

Common Mistakes

Avoid these frequent errors
  • Moving terms without changing signs
    Don't move -3x to the right side as -3x = wrong equation! When you move a term across the equals sign, you must change its sign. Always add 3x to both sides instead of just moving -3x.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I need to move all x-terms to one side?

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Moving all x-terms to one side lets you combine them into a single term like 10x. This makes it easier to isolate x and solve the equation!

Does it matter which side I put the x-terms on?

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No! You can collect x-terms on either side. Choose the side that keeps your coefficients positive to avoid working with negative numbers.

What if I get a negative coefficient for x?

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That's okay! Just divide both sides by the negative number. For example, if you get −5x=15 -5x = 15 , then x=−3 x = -3 .

How do I know when to add or subtract?

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Opposite operations cancel out! To eliminate −3x -3x from the left side, add +3x +3x to both sides. To eliminate −12 -12 from the right side, add +12 +12 to both sides.

Can I check my answer a different way?

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Yes! You can also graph both sides as separate functions and see where they intersect. The x-coordinate of the intersection point is your solution.

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