Solve the Linear Equation: 4X Equals One-Eighth

Q: Why do I divide by 4 instead of subtracting it?

Because 4 is multiplied by x, not added to it! When a number multiplies the variable, you use the opposite operation (division) to isolate x.

Q: How do I divide a fraction by a whole number?

Dividing by a number is the same as multiplying by its reciprocal. So $ \frac{1}{8} ÷ 4 = \frac{1}{8} \times \frac{1}{4} = \frac{1}{32} $.

Q: Is 1/32 really that small?

Yes! $ \frac{1}{32} = 0.03125 $, which is very small. This makes sense because if you multiply a tiny number by 4, you get $ \frac{1}{8} = 0.125 $.

Q: Can I convert everything to decimals instead?

You could, but fractions are often more exact. Converting $ \frac{1}{8} $ to 0.125 and dividing by 4 gives 0.03125, but $ \frac{1}{32} $ is the precise answer.

Q: How do I check my answer?

Substitute $ x = \frac{1}{32} $ back into the original equation: $ 4 \times \frac{1}{32} = \frac{4}{32} = \frac{1}{8} $ ✓. Both sides match!

Linear Equations with Fractional Solutions

Solve for X:

$4x=\frac{1}{8}$

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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

00:19 Let's reduce what we can

00:30 Let's write division as multiplication by the reciprocal

00:38 Make sure to multiply numerator by numerator and denominator by denominator

00:45 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$4x=\frac{1}{8}$

Step-by-step solution

To solve the equation $4x = \frac{1}{8}$ , we need to isolate $x$ . We do this by dividing both sides of the equation by the coefficient of $x$ , which is 4:

Step 1: Write the original equation: $4x = \frac{1}{8}$ .
Step 2: Divide both sides by 4 to solve for $x$ :

$x = \frac{\frac{1}{8}}{4}$

Step 3: Simplify the right-hand side by multiplying fractions, recalling that dividing by a number is equivalent to multiplying by its reciprocal:

$x = \frac{1}{8} \times \frac{1}{4} = \frac{1 \times 1}{8 \times 4} = \frac{1}{32}$

Thus, the solution to the equation is $x = \frac{1}{32}$ .

Final Answer

$\frac{1}{32}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Divide both sides by the coefficient of x
Technique: $\frac{\frac{1}{8}}{4} = \frac{1}{8} \times \frac{1}{4} = \frac{1}{32}$
Check: Substitute back: $4 \times \frac{1}{32} = \frac{4}{32} = \frac{1}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting instead of dividing
Don't try to subtract 4 from both sides when x has a coefficient! This gives $x = \frac{1}{8} - 4 = -\frac{31}{8}$ which is completely wrong. Always divide both sides by the coefficient to isolate x.

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 divide by 4 instead of subtracting it?

Because 4 is multiplied by x, not added to it! When a number multiplies the variable, you use the opposite operation (division) to isolate x.

How do I divide a fraction by a whole number?

Dividing by a number is the same as multiplying by its reciprocal. So $\frac{1}{8} ÷ 4 = \frac{1}{8} \times \frac{1}{4} = \frac{1}{32}$ .

Is 1/32 really that small?

Yes! $\frac{1}{32} = 0.03125$ , which is very small. This makes sense because if you multiply a tiny number by 4, you get $\frac{1}{8} = 0.125$ .

Can I convert everything to decimals instead?

You could, but fractions are often more exact. Converting $\frac{1}{8}$ to 0.125 and dividing by 4 gives 0.03125, but $\frac{1}{32}$ is the precise answer.

How do I check my answer?

Substitute $x = \frac{1}{32}$ back into the original equation: $4 \times \frac{1}{32} = \frac{4}{32} = \frac{1}{8}$ ✓. Both sides match!

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