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

Q: Why do I add 3 instead of subtract 3?

You need to use the opposite operation to cancel out the -3. Since we have -3, we add +3 to both sides. Think of it as undoing what's being done to x.

Q: Can I divide by 5 first instead of adding 3?

You could, but it's messier! You'd get $ x - \frac{3}{5} = \frac{2}{5} $. It's easier to eliminate constants first, then deal with coefficients.

Q: What if I get a negative answer?

Negative answers are perfectly valid! Always check your work by substituting back into the original equation, regardless of whether your answer is positive or negative.

Q: How do I know which operation to do first?

Follow the reverse order of operations! Since multiplication and division happen before addition and subtraction, undo addition/subtraction first, then multiplication/division.

Q: What does 'isolate the variable' mean?

It means getting the variable by itself on one side of the equation. You want $ x = \text{some number} $, not $ 5x - 3 = 2 $.

Linear Equations with Addition and Division Steps

Solve for X:

$5x - 3 = 2$

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Understand the problem

Solve for X:

$5x - 3 = 2$

Step-by-step solution

Step-by-step solution:

1. Begin with the equation: $5x - 3 = 2$

2. Add 3 to both sides: $5x - 3 + 3 = 2 + 3$ , which simplifies to $5x = 5$

3. Divide both sides by 5 to solve for x: $x = \frac{5}{5}$

4. Simplify the division: $x = 1$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Use inverse operations to isolate the variable term
Technique: Add 3 to both sides: 5x - 3 + 3 = 2 + 3
Check: Substitute x = 1: 5(1) - 3 = 2 ✓

Common Mistakes

Avoid these frequent errors

Not performing the same operation on both sides
Don't add 3 to only one side = unequal equation! This breaks the balance and gives incorrect solutions. Always perform identical operations on both sides of the equals sign.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I add 3 instead of subtract 3?

You need to use the opposite operation to cancel out the -3. Since we have -3, we add +3 to both sides. Think of it as undoing what's being done to x.

Can I divide by 5 first instead of adding 3?

You could, but it's messier! You'd get $x - \frac{3}{5} = \frac{2}{5}$ . It's easier to eliminate constants first, then deal with coefficients.

What if I get a negative answer?

Negative answers are perfectly valid! Always check your work by substituting back into the original equation, regardless of whether your answer is positive or negative.

How do I know which operation to do first?

Follow the reverse order of operations! Since multiplication and division happen before addition and subtraction, undo addition/subtraction first, then multiplication/division.

What does 'isolate the variable' mean?

It means getting the variable by itself on one side of the equation. You want $x = \text{some number}$ , not $5x - 3 = 2$ .

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