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

Find the value of the parameter X

$\frac{1}{3}x=\frac{1}{9}$

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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