Solve the Linear Equation: 6-7x=-5x+8 Step by Step

Linear Equations with Variable Terms

Solve for X:

67x=5x+8 6-7x=-5x+8

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:10 Isolate the unknown X
00:25 Reduce what's possible
00:33 Combine like terms
00:41 Continue to isolate the unknown X
00:58 Reduce what's possible
01:02 Continue to isolate the unknown X
01:16 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

67x=5x+8 6-7x=-5x+8

2

Step-by-step solution

To solve the equation 67x=5x+8 6 - 7x = -5x + 8 , we will follow these steps:

  • Step 1: Move all terms involving x x to one side of the equation by adding 5x 5x to both sides.
  • Step 2: Simplify both sides of the equation.
  • Step 3: Solve for x x .

Now, let's work through each step:

Step 1: Add 5x 5x to both sides to move the x x -term to the left side:

67x+5x=8 6 - 7x + 5x = 8

Step 2: Simplify the equation by combining the x x -terms on the left side:

62x=8 6 - 2x = 8

Step 3: To isolate 2x -2x on the left, subtract 6 6 from both sides:

2x=86 -2x = 8 - 6

Simplify the right side:

2x=2 -2x = 2

Finally, divide both sides by 2-2 to solve for x x :

x=22 x = \frac{2}{-2}

x=1 x = -1

Therefore, the solution to the problem is x=1 x = -1 .

3

Final Answer

1 -1

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Move all x-terms to one side, constants to other
  • Technique: Add 5x to both sides: 6 - 7x + 5x = 8
  • Check: Substitute x = -1: 6 - 7(-1) = -5(-1) + 8 gives 13 = 13 ✓

Common Mistakes

Avoid these frequent errors
  • Moving terms without changing signs
    Don't move -7x to the right as -7x = wrong equation! When moving terms across the equals sign, you must change their sign. Always add the opposite: add +7x to both sides to move -7x.

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 add 5x to both sides instead of subtracting 7x?

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Great question! You want to eliminate the negative coefficient on x. Adding 5x to both sides gives you 7x+5x=2x -7x + 5x = -2x , which is easier to work with than having x-terms on both sides.

What if I moved the constants first instead?

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That works too! You could subtract 6 from both sides first, then add 5x. Either approach will give you the same answer - choose whichever feels more comfortable.

How do I know which side to move the x-terms to?

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Move them to whichever side will give you a positive coefficient for x. In this problem, moving to the left side gives 2x -2x , which is fine to work with.

Why is my answer negative?

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Negative answers are completely normal in algebra! The key is to check your work by substituting back. If x=1 x = -1 makes both sides equal, then it's correct.

What if I get confused about which operation to do next?

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Follow this order: 1) Move x-terms to one side, 2) Move constants to the other side, 3) Divide by the coefficient of x. Take it one step at a time!

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