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

Q: Why is my answer a fraction instead of a whole number?

Not all equations have whole number solutions! When 3 doesn't divide evenly by 5, you get a fraction. This is completely normal and correct.

Q: How do I know if 3/5 is in simplest form?

Check if 3 and 5 have any common factors. Since 3 and 5 are both prime numbers with no shared factors except 1, $ \frac{3}{5} $ is already simplified!

Q: Can I convert 3/5 to a decimal?

Yes! $ \frac{3}{5} = 0.6 $. Both forms are correct, but keep fractions unless the problem specifically asks for decimals.

Q: How can I check my work?

Substitute your answer back: $ 5 \times \frac{3}{5} = \frac{15}{5} = 3 $. If you get 3 on both sides, you're correct!

Linear Equations with Fractional Solutions

Solve for X:

$5x=3$

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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

00:16 Let's simplify what we can

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$5x=3$

Step-by-step solution

To solve the equation $5x = 3$ , we will isolate $x$ by using division:

Step 1: Recognize that $x$ is multiplied by 5. To isolate $x$ , we need to undo this multiplication.
Step 2: Divide both sides of the equation by 5. This step uses the Division Property of Equality:

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

Step 3: Simplify both sides. The left side simplifies to $x$ (because $\frac{5x}{5} = x$ ), and the right side is $\frac{3}{5}$ .

Hence, the solution to the equation $5x = 3$ is $x = \frac{3}{5}$ .

Final Answer

$\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Division Property: Divide both sides by the coefficient to isolate x
Technique: Divide 5x = 3 by 5 to get x = 3/5
Check: Substitute back: 5(3/5) = 15/5 = 3 ✓

Common Mistakes

Avoid these frequent errors

Dividing incorrectly or switching numerator and denominator
Don't divide 3 by 5 and write x = 5/3! This flips the fraction and gives the wrong answer. Always divide the number by the coefficient: 3 ÷ 5 = 3/5.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why is my answer a fraction instead of a whole number?

Not all equations have whole number solutions! When 3 doesn't divide evenly by 5, you get a fraction. This is completely normal and correct.

How do I know if 3/5 is in simplest form?

Check if 3 and 5 have any common factors. Since 3 and 5 are both prime numbers with no shared factors except 1, $\frac{3}{5}$ is already simplified!

Can I convert 3/5 to a decimal?

Yes! $\frac{3}{5} = 0.6$ . Both forms are correct, but keep fractions unless the problem specifically asks for decimals.

What if I accidentally wrote x = 5/3?

That's a common mistake! Remember: when you divide 3 by 5, you get $\frac{3}{5}$ , not $\frac{5}{3}$ . The number being divided goes on top.

How can I check my work?

Substitute your answer back: $5 \times \frac{3}{5} = \frac{15}{5} = 3$ . If you get 3 on both sides, you're correct!

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