Solve for X in the Linear Equation: 5 - x = 12 - 4

Linear Equations with Negative Solutions

Solve for X:

5x=124 5 - x = 12 - 4

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1

Understand the problem

Solve for X:

5x=124 5 - x = 12 - 4

2

Step-by-step solution

First, simplify the right side of the equation:
124=8 12 - 4 = 8
Hence, the equation becomes 5x=8 5 - x = 8 .
Subtract 5 from both sides to isolate x x :
5x5=85 5 - x - 5 = 8 - 5
This simplifies to:
x=3 -x=3
Divide by -1 to solve for x x :
x=3 x=-3
Therefore, the solution is x=3 x=-3 .

3

Final Answer

-3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Simplify the right side of the equation first
  • Technique: Subtract 5 from both sides: 5 - x - 5 = 8 - 5
  • Check: Substitute x = -3: 5 - (-3) = 5 + 3 = 8 ✓

Common Mistakes

Avoid these frequent errors
  • Adding 5 to both sides instead of subtracting
    Don't add 5 to both sides when you have 5 - x = 8! This gives you -x = 13 instead of -x = 3, leading to x = -13 which is wrong. Always subtract the constant term that's being added to the variable term.

Practice Quiz

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\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why is the answer negative when both sides of the original equation are positive?

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The answer is negative because we're subtracting x on the left side! When 5 - x = 8, we need x to be negative so that subtracting it (which means adding its positive value) gives us 8.

Do I always subtract the number next to x?

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Not always! Look at the operation. If you have 5 - x, subtract 5. If you have 5 + x, subtract 5. The goal is to isolate the x term on one side.

What does -x = 3 mean exactly?

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It means negative x equals 3. To find x, you need to multiply both sides by -1, which gives you x = -3. Think of it as: what number, when made negative, equals 3?

Can I move the x to the right side instead?

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Yes! You can add x to both sides: 5=8+x 5 = 8 + x , then subtract 8: 3=x -3 = x . Both methods work and give the same answer.

How do I check my answer when there are negative numbers?

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Substitute carefully! For x = -3: 5(3)=5+3=8 5 - (-3) = 5 + 3 = 8 and 124=8 12 - 4 = 8 . Both sides equal 8, so it's correct!

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