Solve the Linear Equation: Uncovering X in 8x = 5

Q: Why can't I just move the 8 to the other side?

You can think of it that way! When you divide both sides by 8, it's the same as moving the 8 from the left side to the right side as a divisor. Both methods give $ x = \frac{5}{8} $.

Q: Should I convert the fraction to a decimal?

Keep it as a fraction! $ \frac{5}{8} $ is the exact answer. Converting to 0.625 might introduce rounding errors in further calculations.

Q: How do I know if 5/8 is in simplest form?

Check if 5 and 8 share any common factors. Since 5 is prime and doesn't divide 8, $ \frac{5}{8} $ is already in simplest form.

Q: What if the coefficient was negative, like -8x = 5?

Same process! Divide both sides by -8: $ x = \frac{5}{-8} = -\frac{5}{8} $. The negative sign makes your answer negative.

Q: Can I multiply both sides by 1/8 instead of dividing by 8?

Absolutely! Multiplying by $ \frac{1}{8} $ is the same as dividing by 8. Both give you $ x = \frac{5}{8} $.

Linear Equations with Fractional Solutions

Solve for X:

$8x=5$

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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

00:07 Let's arrange the equation so that one side has only the unknown X

00:12 Let's reduce what we can

00:17 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:

$8x=5$

Step-by-step solution

To solve the equation $8x = 5$ , follow these steps:

Step 1: Identify the equation $8x = 5$ , where $x$ is the unknown variable.
Step 2: To isolate $x$ , divide both sides of the equation by 8.
This step involves equivalent operations to maintain equality.
Step 3: Perform the division on both sides:
$\frac{8x}{8} = \frac{5}{8}$ .
This simplifies to $x = \frac{5}{8}$ .

Now, let's outline these steps in detail:

We begin with the equation $8x = 5$ .

Dividing both sides by the coefficient of $x$ , which is 8, gives:

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

This simplifies directly to:

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

Therefore, the solution to the problem is $x = \frac{5}{8}$ .

Final Answer

$\frac{5}{8}$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Divide both sides by the coefficient of x
Division Technique: $\frac{8x}{8} = \frac{5}{8}$ simplifies to $x = \frac{5}{8}$
Verification: Substitute back: $8 \times \frac{5}{8} = 5$ ✓

Common Mistakes

Avoid these frequent errors

Dividing only the left side by the coefficient
Don't divide just 8x by 8 and leave 5 unchanged = $x = 5$ ! This breaks the equality because you didn't perform the same operation on both sides. Always divide both sides by the same number to maintain balance.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why can't I just move the 8 to the other side?

You can think of it that way! When you divide both sides by 8, it's the same as moving the 8 from the left side to the right side as a divisor. Both methods give $x = \frac{5}{8}$ .

Should I convert the fraction to a decimal?

Keep it as a fraction! $\frac{5}{8}$ is the exact answer. Converting to 0.625 might introduce rounding errors in further calculations.

How do I know if 5/8 is in simplest form?

Check if 5 and 8 share any common factors. Since 5 is prime and doesn't divide 8, $\frac{5}{8}$ is already in simplest form.

What if the coefficient was negative, like -8x = 5?

Same process! Divide both sides by -8: $x = \frac{5}{-8} = -\frac{5}{8}$ . The negative sign makes your answer negative.

Can I multiply both sides by 1/8 instead of dividing by 8?

Absolutely! Multiplying by $\frac{1}{8}$ is the same as dividing by 8. Both give you $x = \frac{5}{8}$ .

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