Solve the Equation: Finding X in 5x × 6 = 90

Q: Should I multiply 5x and 6 first or divide by something first?

Always multiply first! Combine $ 5x \cdot 6 $ to get $ 30x $. This gives you the clearest path: $ 30x = 90 $, so $ x = 3 $.

Q: Why can't I just divide 90 by 5 to get x = 18?

Because you have $ 5x \cdot 6 $, not just $ 5x $! The coefficient of x is actually 30 (since 5 × 6 = 30). You must account for both numbers multiplying x.

Q: What if I divided by 6 first instead of multiplying?

That works too! $ 5x \cdot 6 = 90 $ becomes $ 5x = 15 $ when you divide both sides by 6. Then $ x = 3 $. Both methods give the same answer!

Q: What does the dot between 5x and 6 mean?

The dot (·) means multiplication, just like × or no symbol at all. So $ 5x \cdot 6 $ means $ 5x \times 6 $ or simply $ 5x(6) $.

Linear Equations with Multiplication and Division

Solve the equation:

$5x \cdot 6 = 90$

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Understand the problem

Solve the equation:

$5x \cdot 6 = 90$

Step-by-step solution

To solve the equation $5x \cdot 6 = 90$ , start by simplifying the left side of the equation:

Divide both sides by 6 to isolate $5x$ :

$5x = \frac{90}{6}$

This simplifies to:

$5x = 15$

Next, divide both sides by 5 to solve for $x$ :

$x = \frac{15}{5}$

This gives us:

$x = 3$

Final Answer

$x=3$

Key Points to Remember

Essential concepts to master this topic

Rule: Use inverse operations to isolate the variable term
Technique: First simplify $5x \cdot 6 = 30x$ , then divide by 30
Check: Substitute back: $5(3) \cdot 6 = 30 \cdot 6 = 90$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by only one factor at a time
Don't divide by 5 first to get $x \cdot 6 = 18$ then by 6 = wrong steps! This creates unnecessary work and confusion. Always simplify the coefficient of x first: $5x \cdot 6 = 30x$ , then divide both sides by 30.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Should I multiply 5x and 6 first or divide by something first?

Always multiply first! Combine $5x \cdot 6$ to get $30x$ . This gives you the clearest path: $30x = 90$ , so $x = 3$ .

Why can't I just divide 90 by 5 to get x = 18?

Because you have $5x \cdot 6$ , not just $5x$ ! The coefficient of x is actually 30 (since 5 × 6 = 30). You must account for both numbers multiplying x.

What if I divided by 6 first instead of multiplying?

That works too! $5x \cdot 6 = 90$ becomes $5x = 15$ when you divide both sides by 6. Then $x = 3$ . Both methods give the same answer!

How do I know which method is easier?

Choose based on the numbers! If one factor divides evenly into the right side (like 6 divides into 90), start there. Otherwise, multiply the coefficients first for clarity.

What does the dot between 5x and 6 mean?

The dot (·) means multiplication, just like × or no symbol at all. So $5x \cdot 6$ means $5x \times 6$ or simply $5x(6)$ .

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