Solve for X in the Equation: 3-x+7=5 | Linear Equation Solution

Linear Equations with Negative Coefficients

Solve for X:

3x+7=5 3-x+7=5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve the problem step by step.
00:08 First, collect all like terms together.
00:16 Next, isolate the unknown variable X on one side of the equation.
00:30 Now, reduce or simplify what we can.
00:40 Convert any negative numbers into positive numbers.
00:52 Remember, a negative times a negative is positive.
00:56 And there you have it! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

3x+7=5 3-x+7=5

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Simplify the given equation by combining like terms.
  • Step 2: Isolate the variable x x on one side of the equation.
  • Step 3: Solve the resulting simplified equation for x x .

Now, let's work through each step:

Step 1: Simplify the given equation:

The original equation is: 3x+7=5 3 - x + 7 = 5 .

Combine like terms on the left side of the equation:

3+7=10 3 + 7 = 10 , so the equation becomes:

10x=5 10 - x = 5 .

Step 2: Isolate the variable x x :

Subtract 10 from both sides of the equation to move the constant term:

x=510 -x = 5 - 10 .

Simplify the right side:

x=5 -x = -5 .

Step 3: Solve for x x :

Multiply both sides of the equation by 1-1 to solve for x x :

x=5 x = 5 .

Therefore, the solution to the problem is x=5 x = 5 .

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Combine like terms first to simplify the equation
  • Technique: Subtract 10 from both sides: -x = -5
  • Check: Substitute x = 5: 3 - 5 + 7 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to combine like terms before solving
    Don't jump straight to isolating x without combining 3 + 7 = 10 first! This leads to messy algebra with multiple unnecessary steps. Always combine like terms on each side before moving variables or constants.

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 combine 3 and 7 first instead of moving x right away?

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Combining like terms first makes the equation simpler! Instead of working with 3 - x + 7 = 5, you get the cleaner 10 - x = 5, which is much easier to solve.

What do I do when I get -x = -5?

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When you have negative x, multiply both sides by -1 to make x positive. So -x = -5 becomes x = 5. Remember: multiplying by -1 flips the signs on both sides!

How can I check if x = 5 is really correct?

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Substitute x = 5 back into the original equation: 3 - 5 + 7 = 5. Calculate step by step: 3 - 5 = -2, then -2 + 7 = 5. Since 5 = 5, your answer is correct!

Why don't I add x to both sides instead of subtracting 10?

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Both methods work! You could add x to get 10 = 5 + x, then subtract 5. But subtracting 10 from both sides is often more direct when you have a negative x term.

What if I accidentally wrote 10 + x = 5 instead of 10 - x = 5?

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Be careful with signs! The original equation has -x, not +x. When combining 3 - x + 7, you get 3 + 7 - x = 10 - x. Always double-check your signs when combining terms.

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