Solve for X in the Equation: 1/5x - 4 = 6

Q: Why do I add 4 first instead of multiplying by 5?

Following the reverse order of operations makes solving easier! Since we subtract 4 in the original equation, we undo that first. Then we handle the fraction multiplication.

Q: What if the fraction was negative like -1/5x?

The steps stay the same! Just be careful with your negative signs. When you multiply both sides by 5, the negative stays: $ -x = \text{result} $, so divide by -1 at the end.

Q: Can I multiply by 5 first instead of adding 4?

Yes, but it's messier! You'd get $ x - 20 = 30 $, which still works but creates larger numbers. The isolate constants first method keeps numbers smaller.

Q: How do I check my answer is definitely correct?

Substitute x = 50 back into the original equation: $ \frac{1}{5}(50) - 4 = 10 - 4 = 6 $ ✓. If both sides equal 6, you solved it correctly!

Q: What if I get a decimal answer instead of a whole number?

That's perfectly normal! Many linear equations have decimal or fractional solutions. Just make sure to substitute your exact answer back to verify it works.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:08 Let's arrange the equation so that one side has only the unknown X

00:17 Let's simplify what we can

00:26 Let's isolate the unknown X and calculate

00:40 And this is 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:

$\frac{1}{5}x-4=6$

2

Step-by-step solution

To solve the equation $\frac{1}{5}x - 4 = 6$ , we will follow these steps:

Step 1: Add 4 to both sides of the equation to eliminate the subtraction and isolate the fractional term.
Step 2: Multiply both sides by 5 to clear the fraction and solve for $x$ .

Let's apply these steps to solve the equation:

Step 1: Add 4 to both sides:
$\frac{1}{5}x - 4 + 4 = 6 + 4$
This simplifies to:
$\frac{1}{5}x = 10$

Step 2: Multiply both sides by 5 to solve for $x$ :
$5 \times \frac{1}{5}x = 10 \times 5$
This simplifies to:
$x = 50$

Therefore, the solution to the equation is $x = 50$ .

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic

Addition Property: Add opposite constant to both sides first
Technique: Multiply both sides by 5 to eliminate $\frac{1}{5}$
Check: Substitute x = 50: $\frac{1}{5}(50) - 4 = 6$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the fractional term by 5
Don't multiply just $\frac{1}{5}x$ by 5 and leave -4 unchanged = unbalanced equation! This breaks the equality rule and gives wrong answers like x = 2. Always multiply every term on both sides by the same number.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I add 4 first instead of multiplying by 5?

+

Following the reverse order of operations makes solving easier! Since we subtract 4 in the original equation, we undo that first. Then we handle the fraction multiplication.

What if the fraction was negative like -1/5x?

+

The steps stay the same! Just be careful with your negative signs. When you multiply both sides by 5, the negative stays: $-x = \text{result}$ , so divide by -1 at the end.

Can I multiply by 5 first instead of adding 4?

+

Yes, but it's messier! You'd get $x - 20 = 30$ , which still works but creates larger numbers. The isolate constants first method keeps numbers smaller.

How do I check my answer is definitely correct?

+

Substitute x = 50 back into the original equation: $\frac{1}{5}(50) - 4 = 10 - 4 = 6$ ✓. If both sides equal 6, you solved it correctly!

What if I get a decimal answer instead of a whole number?

+

That's perfectly normal! Many linear equations have decimal or fractional solutions. Just make sure to substitute your exact answer back to verify it works.

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Solve for X in the Equation: 1/5x - 4 = 6

Linear Equations with Fractional Coefficients

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I add 4 first instead of multiplying by 5?

What if the fraction was negative like -1/5x?

Can I multiply by 5 first instead of adding 4?

How do I check my answer is definitely correct?

What if I get a decimal answer instead of a whole number?

🌟 Unlock Your Math Potential

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