Solve for X: Finding the Solution to 4x - 7 = x + 5

Linear Equations with Variable Isolation

Solve for X:

4x7=x+5 4x - 7 = x + 5

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1

Understand the problem

Solve for X:

4x7=x+5 4x - 7 = x + 5

2

Step-by-step solution

To solve forx x , first, get all terms involving x x on one side and constants on the other. Start from:

4x7=x+5 4x - 7 = x + 5

Subtract x x from both sides to simplify:

3x7=5 3x - 7 = 5

Add 7 to both sides to isolate the terms withx x :

3x=12 3x = 12

Divide each side by 3 to solve forx x :

x=4 x = 4

Thus, x x is 4 4 .

3

Final Answer

4 4

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Move all x terms to one side, constants to other
  • Technique: Subtract x from both sides: 4x - x = 3x
  • Check: Substitute x = 4: 4(4) - 7 = 16 - 7 = 9, and 4 + 5 = 9 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting when moving terms
    Don't add x to both sides when you see 4x - 7 = x + 5, giving 5x - 7 = 5 = wrong answer! This keeps x on both sides instead of isolating it. Always subtract the smaller x term from both sides to collect variables on one side.

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 x from both sides instead of adding it?

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We want to collect all x terms on one side. Since we have 4x on the left and x on the right, subtracting x from both sides gives us 3x on the left and 0x on the right - much cleaner!

What if I move the 4x to the right side instead?

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That works too! You'd get 7=3x+5 -7 = -3x + 5 , then solve to get the same answer. Choose whichever keeps your coefficient positive - it's less confusing.

How do I remember which operations to use?

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Think "opposite operations": if you see +5, subtract 5 from both sides. If you see -7, add 7 to both sides. You're undoing what's been done to x!

What's the difference between 3x = 12 and x = 4?

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3x=12 3x = 12 means "3 times some number equals 12." To find that number, divide both sides by 3 to get x=4 x = 4 .

Can I check my answer a different way?

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Yes! You can also graph both sides as separate lines: y = 4x - 7 and y = x + 5. Where they intersect is your solution: (4, 9).

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