Solve Linear Equation: Finding X in 5 + x - 3 = 2 + 1

Linear Equations with Simplification Steps

Solve for X:

5+x3=2+1 5 + x - 3 = 2 + 1

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Understand the problem

Solve for X:

5+x3=2+1 5 + x - 3 = 2 + 1

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Step-by-step solution

To solve 5+x3=2+1 5 + x - 3 = 2 + 1 , we first simplify both sides:

Left side:
53+x=2+x 5 - 3 + x = 2 + x

Right side:
2+1=3 2 + 1 = 3

Now the equation is 2+x=3 2 + x = 3 .

Subtract 2 from both sides:
x=32 x = 3 - 2

So, x=1 x = 1 .

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Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Order: Simplify both sides first before isolating the variable
  • Technique: Combine like terms: 5 - 3 = 2, so 2 + x = 3
  • Check: Substitute x = 1: 5 + 1 - 3 = 3 and 2 + 1 = 3 ✓

Common Mistakes

Avoid these frequent errors
  • Rushing to isolate x without simplifying first
    Don't try to isolate x from 5 + x - 3 = 2 + 1 immediately = messy work and errors! This skips the crucial simplification step and makes the problem harder than it needs to be. Always simplify both sides completely before solving for the variable.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just move x to one side right away?

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You could, but it's much easier to simplify first! When you have 5 + x - 3 = 2 + 1, combining like terms gives you 2 + x = 3, which is much cleaner to work with.

What if I get confused about which terms to combine?

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Look for constant numbers (numbers without variables). On the left side: 5 and -3 combine to make 2. On the right side: 2 and 1 combine to make 3. Leave x alone until after simplifying!

Do I always have to simplify both sides?

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Yes, always! Simplifying makes the equation easier to solve and helps you avoid mistakes. It's like cleaning your workspace before starting a project.

How do I know if I simplified correctly?

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Check that you've combined all the like terms you can. Constants go with constants, and variables stay separate. If you see 2 + x = 3, you know you're ready to solve!

What if my final answer doesn't look right?

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Always substitute your answer back into the original equation! If x = 1, then 5 + 1 - 3 should equal 2 + 1. Both sides equal 3, so x = 1 is correct!

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