Solve the Fraction Equation: Isolating X in 2/9x = 21

Q: What exactly is a reciprocal and why do I need it?

A reciprocal is a fraction flipped upside down! For $ \frac{2}{9} $, the reciprocal is $ \frac{9}{2} $. When you multiply them together, you get 1, which cancels out the coefficient perfectly.

Q: Why can't I just divide both sides by 2/9?

You absolutely can! Dividing by $ \frac{2}{9} $ is the same thing as multiplying by $ \frac{9}{2} $. Both methods work perfectly - choose whichever feels more comfortable to you.

Q: How do I multiply 9/2 times 21?

Think of 21 as $ \frac{21}{1} $, then multiply: $ \frac{9}{2} \times \frac{21}{1} = \frac{9 \times 21}{2 \times 1} = \frac{189}{2} = 94.5 $

Q: How can I check if 94.5 is really correct?

Substitute back: $ \frac{2}{9} \times 94.5 $. Calculate: $ \frac{2 \times 94.5}{9} = \frac{189}{9} = 21 $ ✓ Perfect match!

Linear Equations with Fractional Coefficients

Solve for X:

$\frac{2}{9}x=21$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's start by solving this problem.

00:08 First, we need to isolate the unknown variable X.

00:12 To do this, we'll multiply by the reciprocal. This will help eliminate the fraction.

00:20 Now, let's simplify everything we can.

00:29 And there you have it! This is the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$\frac{2}{9}x=21$

Step-by-step solution

To solve the equation $\frac{2}{9}x = 21$ , we will follow these steps:

Step 1: Multiply each side of the equation by the reciprocal of $\frac{2}{9}$ , which is $\frac{9}{2}$ .
Step 2: Simplify the resulting expression to solve for $x$ .

Let's begin with Step 1:
We have $\frac{2}{9}x = 21$ . To isolate $x$ , multiply both sides of the equation by $\frac{9}{2}$ :

$\frac{9}{2} \cdot \frac{2}{9}x = \frac{9}{2} \cdot 21$

Simplifying the left side, the $\frac{9}{2}$ and $\frac{2}{9}$ cancel each other, leaving $x$ :

$x = \frac{9}{2} \cdot 21$

Now, proceed with Step 2:
Calculate the right-hand side:

$x = \frac{9 \times 21}{2} = \frac{189}{2} = 94.5$

Therefore, the value of $x$ is $\boxed{94.5}$ .

Final Answer

$94.5$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by the reciprocal of the coefficient
Technique: Use $\frac{9}{2} \times \frac{2}{9} = 1$ to isolate x
Check: Substitute x = 94.5: $\frac{2}{9} \times 94.5 = 21$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting to isolate x instead of multiplying
Don't try to subtract $\frac{2}{9}$ from both sides = this doesn't isolate x! Addition/subtraction won't eliminate the fractional coefficient. Always multiply both sides by the reciprocal to cancel the coefficient completely.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

What exactly is a reciprocal and why do I need it?

A reciprocal is a fraction flipped upside down! For $\frac{2}{9}$ , the reciprocal is $\frac{9}{2}$ . When you multiply them together, you get 1, which cancels out the coefficient perfectly.

Why can't I just divide both sides by 2/9?

You absolutely can! Dividing by $\frac{2}{9}$ is the same thing as multiplying by $\frac{9}{2}$ . Both methods work perfectly - choose whichever feels more comfortable to you.

How do I multiply 9/2 times 21?

Think of 21 as $\frac{21}{1}$ , then multiply: $\frac{9}{2} \times \frac{21}{1} = \frac{9 \times 21}{2 \times 1} = \frac{189}{2} = 94.5$

What if I get a different answer like 189?

If you got 189, you probably forgot to divide by 2! Remember: $\frac{189}{2} = 94.5$ . Always complete the final division step when working with fractions.

How can I check if 94.5 is really correct?

Substitute back: $\frac{2}{9} \times 94.5$ . Calculate: $\frac{2 \times 94.5}{9} = \frac{189}{9} = 21$ ✓ Perfect match!

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