Solve for X: Finding the Solution to (x - 3 + 5 = 8 - 2)

Linear Equations with Multiple Operations

Solve for X:

x3+5=82 x - 3 + 5 = 8 - 2

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1

Understand the problem

Solve for X:

x3+5=82 x - 3 + 5 = 8 - 2

2

Step-by-step solution

First, simplify both sides of the equation:

Left side: x3+5=x+2 x - 3 + 5 = x + 2

Right side: 82=6 8 - 2 = 6

Now the equation is: x+2=6 x + 2 = 6

Subtract 2 from both sides to isolate x x :

x+22=62 x + 2 - 2 = 6 - 2

Simplifying gives:

x=4 x = 4

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Simplify both sides before isolating the variable
  • Technique: Combine like terms: x - 3 + 5 becomes x + 2
  • Check: Substitute x = 4: 4 - 3 + 5 = 8 - 2 → 6 = 6 ✓

Common Mistakes

Avoid these frequent errors
  • Not simplifying before isolating x
    Don't work with x - 3 + 5 = 8 - 2 in this messy form = confusing steps and wrong answers! This makes the problem much harder than needed. Always simplify both sides first to get x + 2 = 6.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Should I simplify the left side or right side first?

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It doesn't matter which side you start with! The key is to simplify both sides completely before trying to isolate x. This makes the equation much cleaner to work with.

Why do I get the wrong answer when I don't simplify first?

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When you skip simplifying, you might accidentally combine wrong terms or make calculation errors. Working with x3+5=82 x - 3 + 5 = 8 - 2 directly is much more confusing than x+2=6 x + 2 = 6 !

How do I combine -3 + 5 correctly?

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Think of it as starting with -3 and adding 5: -3 + 5 = +2. You can also use a number line: start at -3, move 5 steps right to reach +2.

What if I solve it without simplifying first?

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You could solve it, but it's much harder! You'd need to add 3 to both sides, then subtract 5, making multiple steps instead of one clean step.

How do I check my answer is correct?

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Substitute x = 4 into the original equation: 4 - 3 + 5 should equal 8 - 2. Both sides give 6, so your answer is right!

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