Solve for X in 7x - 3 = 4x + 9: Linear Equation Practice

Linear Equations with Variable Terms

Solve for X:

7x3=4x+9 7x - 3 = 4x + 9

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1

Understand the problem

Solve for X:

7x3=4x+9 7x - 3 = 4x + 9

2

Step-by-step solution

To solve the equation 7x3=4x+9 7x - 3 = 4x + 9 , follow these steps:

1. Subtract 4x 4x from both sides to get:

7x4x3=9 7x - 4x - 3 = 9

2. Simplify the equation:

3x3=9 3x - 3 = 9

3. Add 3 3 to both sides:

3x=12 3x = 12

4. Divide both sides by 3 3 :

x=4 x=4

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Move all variable terms to one side, constants to the other
  • Technique: Subtract 4x from both sides: 7x - 4x = 3x
  • Check: Substitute x = 4: 7(4) - 3 = 4(4) + 9 gives 25 = 25 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting like terms
    Don't add 7x + 4x = 11x when moving terms = wrong variable coefficient! This doubles the variable instead of isolating it. Always subtract the smaller variable term from both sides to collect like terms properly.

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 subtract 4x from both sides instead of adding?

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You want to isolate x by getting all x-terms on one side. Since 7x is bigger than 4x, subtract 4x from both sides to get 3x 3x on the left and eliminate x from the right side.

What if I move the constants first instead?

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That works too! You could add 3 to both sides first, then subtract 4x. The important thing is to keep the equation balanced - whatever you do to one side, do to the other.

How do I know which side to collect the x terms on?

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Choose the side with the larger coefficient! Since 7x > 4x, keep the x terms on the left side. This avoids negative coefficients and makes the math easier.

What does 'isolate x' actually mean?

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Isolating x means getting x by itself on one side of the equation. You'll have x= x = [some number] when you're done solving.

Can I check my answer a different way?

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Yes! You can also work backwards: if x = 4, then the left side is 7(4) - 3 = 28 - 3 = 25, and the right side is 4(4) + 9 = 16 + 9 = 25. Both sides equal 25, so x = 4 is correct!

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