Solve for X: Finding the Value in -1/3x + 5 = 6/9x

Q: Why do I need to simplify 6/9 to 2/3 first?

Simplifying makes the math easier! Working with 2/3 instead of 6/9 means smaller numbers and cleaner calculations. It's the same value, but much simpler to work with.

Q: How do I add fractions with the same denominator like 2/3x + 1/3x?

When fractions have the same denominator, just add the numerators: $ \frac{2}{3}x + \frac{1}{3}x = \frac{2+1}{3}x = \frac{3}{3}x = x $

Q: What if I move the wrong term to the other side?

No problem! You can move any term to either side as long as you change its sign. The goal is to get all x-terms on one side and constants on the other.

Q: How do I check my answer x = 5?

Substitute x = 5 into the original equation:Left side: $ -\frac{1}{3}(5) + 5 = -\frac{5}{3} + \frac{15}{3} = \frac{10}{3} $Right side: $ \frac{6}{9}(5) = \frac{30}{9} = \frac{10}{3} $Both sides equal $ \frac{10}{3} $, so x = 5 is correct!

Q: Can I multiply everything by 3 to clear the fractions?

Yes! Multiplying both sides by 3 gives: $ -x + 15 = 2x $, which leads to the same answer x = 5. This is often easier than working with fractions.

Linear Equations with Fractional Coefficients

Solve for X:

$-\frac{1}{3}x+5=\frac{6}{9}x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:10 First, we'll isolate the unknown variable, X.

00:28 Now, let's simplify any part of the equation that we can.

00:37 For example, factor six into two times three.

00:44 Next, factor nine into three times three.

00:51 Simplify the expression some more.

01:03 Great job! And that's how we find 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:

$-\frac{1}{3}x+5=\frac{6}{9}x$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Manipulate the equation to consolidate terms involving $x$ .
Step 2: Simplify the equation by fixing fractions.
Step 3: Solve for $x$ to find the solution.

Now, let's work through each step:
Step 1: Start with the original equation, $-\frac{1}{3}x + 5 = \frac{6}{9}x$ . First, simplify $\frac{6}{9}$ to $\frac{2}{3}$ , giving us the equivalent equation:
$-\frac{1}{3}x + 5 = \frac{2}{3}x.$

Step 2: Move the $-\frac{1}{3}x$ term to the right side to consolidate terms,
$5 = \frac{2}{3}x + \frac{1}{3}x.$

Step 3: Simplify the terms involving $x$ on the right side. $\frac{2}{3}x + \frac{1}{3}x = \frac{3}{3}x = x.$ Thus, the equation becomes:
$5 = x.$

Therefore, the solution to the equation is $x = 5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Simplify First: Convert 6/9 to 2/3 before solving the equation
Combine Terms: Move -1/3x to right: 2/3x + 1/3x = 3/3x = x
Verification: Substitute x = 5: -1/3(5) + 5 = -5/3 + 15/3 = 10/3 = 6/9(5) ✓

Common Mistakes

Avoid these frequent errors

Not simplifying fractions before solving
Don't leave 6/9 unsimplified throughout the problem = more complex calculations and higher chance of errors! Working with 6/9 instead of 2/3 makes addition harder and creates unnecessary complexity. Always simplify fractions to lowest terms at the start.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to simplify 6/9 to 2/3 first?

Simplifying makes the math easier! Working with 2/3 instead of 6/9 means smaller numbers and cleaner calculations. It's the same value, but much simpler to work with.

How do I add fractions with the same denominator like 2/3x + 1/3x?

When fractions have the same denominator, just add the numerators: $\frac{2}{3}x + \frac{1}{3}x = \frac{2+1}{3}x = \frac{3}{3}x = x$

What if I move the wrong term to the other side?

No problem! You can move any term to either side as long as you change its sign. The goal is to get all x-terms on one side and constants on the other.

How do I check my answer x = 5?

Substitute x = 5 into the original equation:

Left side: $-\frac{1}{3}(5) + 5 = -\frac{5}{3} + \frac{15}{3} = \frac{10}{3}$
Right side: $\frac{6}{9}(5) = \frac{30}{9} = \frac{10}{3}$
Both sides equal $\frac{10}{3}$ , so x = 5 is correct!

Can I multiply everything by 3 to clear the fractions?

Yes! Multiplying both sides by 3 gives: $-x + 15 = 2x$ , which leads to the same answer x = 5. This is often easier than working with fractions.

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