Solve the Linear Equation: Finding X in -5 + X = -3

Linear Equations with Negative Constants

Solve for X:

−5+x=−3 -5+x=-3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this step-by-step.
00:08 First, we'll find the value of X by isolating it on one side of the equation.
00:24 Next, we'll simplify everything to make it easier to understand.
00:30 And there you go! That's how you find 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:

−5+x=−3 -5+x=-3

2

Step-by-step solution

To solve the equation −5+x=−3-5 + x = -3, we can follow these steps:

  • Step 1: We want to isolate x x on one side of the equation. Currently, it is subtracted by 5, so we'll eliminate the -5 by performing the operation of addition.
  • Step 2: Add 5 to both sides of the equation to cancel out the -5:
    −5+x+5=−3+5-5 + x + 5 = -3 + 5
  • Step 3: Simplify both sides:
    x=−3+5x = -3 + 5
  • Step 4: Perform the arithmetic operation on the right side:
    x=2x = 2

Therefore, the solution to the problem is x=2 x = 2 .

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Add the same value to both sides to isolate x
  • Technique: Add 5 to both sides: −5+x+5=−3+5-5 + x + 5 = -3 + 5
  • Check: Substitute back: −5+2=−3-5 + 2 = -3 gives −3=−3-3 = -3 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting to cancel negative terms
    Don't subtract 5 from both sides when you see -5 + x = adding 5 instead gives x = -8! The negative sign is already part of -5, so you need to add +5 to cancel it out. Always add the opposite of what you want to eliminate.

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 5 instead of subtract 5?

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You have -5 + x, and you want to get rid of the -5. The opposite of -5 is +5, so adding 5 to both sides cancels out the -5 perfectly!

What if I get confused about positive and negative signs?

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Think of it like a balance scale! Whatever you do to one side, you must do to the other. To cancel out -5, you need to add +5 to both sides.

How can I check if x = 2 is correct?

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Substitute 2 back into the original equation: −5+2=−3-5 + 2 = -3. Since -3 = -3 is true, your answer is correct!

What's the difference between -5 + x and 5 - x?

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-5 + x means "negative 5 plus x" while 5 - x means "5 minus x". These are completely different expressions with different solutions!

Can I solve this equation a different way?

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You could rewrite it as x−5=−3x - 5 = -3, then add 5 to both sides. Both methods work, but make sure to keep track of your signs!

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