Solve for X in the Equation: 5x = 3/8

Q: Why do I divide by 5 instead of multiply?

You need to isolate x by getting rid of the 5 that's multiplying it. The opposite of multiplication is division, so you divide both sides by 5.

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

Dividing by a whole number is the same as multiplying by its reciprocal. So $ \frac{3}{8} ÷ 5 = \frac{3}{8} \times \frac{1}{5} = \frac{3}{40} $.

Q: How do I know if my fraction answer is simplified?

Check if the numerator and denominator have any common factors. Since 3 and 40 share no common factors other than 1, $ \frac{3}{40} $ is already in simplest form.

Q: What if I get confused about which operation to use?

Remember: you want to undo what's being done to x. Since x is being multiplied by 5, you need to divide by 5 to cancel it out.

Linear Equations with Fractional Constants

Solve for X:

$5x=\frac{3}{8}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve the equation step by step.

00:08 We need to isolate X, the unknown, by itself.

00:14 If the unknown X has a coefficient A, it equals C divided b y B.

00:20 To isolate X, divide both sides by A.

00:25 Let's apply this formula to our exercise.

00:30 Rearrange the equation, so that X is alone on one side.

00:36 Now, let's calculate the denominator to simplify.

00:40 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$5x=\frac{3}{8}$

Step-by-step solution

$ax=\frac{c}{b}$

$x=\frac{c}{b\cdot a}$

Final Answer

$\frac{3}{40}$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Divide both sides by the coefficient of x
Technique: Divide $\frac{3}{8}$ by 5 to get $\frac{3}{8} \times \frac{1}{5} = \frac{3}{40}$
Check: Substitute back: $5 \times \frac{3}{40} = \frac{15}{40} = \frac{3}{8}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying both sides by 5 instead of dividing
Don't multiply both sides by 5 to get $25x = \frac{15}{8}$ ! This makes the equation more complex and leads to wrong answers. Always divide both sides by the coefficient to isolate x.

Practice Quiz

Test your knowledge with interactive questions

$$ 4=3y $$

FAQ

Everything you need to know about this question

Why do I divide by 5 instead of multiply?

You need to isolate x by getting rid of the 5 that's multiplying it. The opposite of multiplication is division, so you divide both sides by 5.

How do I divide a fraction by a whole number?

Dividing by a whole number is the same as multiplying by its reciprocal. So $\frac{3}{8} ÷ 5 = \frac{3}{8} \times \frac{1}{5} = \frac{3}{40}$ .

Can I convert the fraction to a decimal first?

You could, but it's usually easier to keep it as a fraction. Converting $\frac{3}{8}$ to 0.375 and then dividing by 5 gives 0.075, but $\frac{3}{40}$ is the exact answer.

How do I know if my fraction answer is simplified?

Check if the numerator and denominator have any common factors. Since 3 and 40 share no common factors other than 1, $\frac{3}{40}$ is already in simplest form.

What if I get confused about which operation to use?

Remember: you want to undo what's being done to x. Since x is being multiplied by 5, you need to divide by 5 to cancel it out.

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