Solve the Linear Equation: Finding X in 13-2x=0

Q: Why do I subtract 13 from both sides first?

You need to isolate the term with x before dividing. If you divide first, you'd have messy fractions to work with. Always move constants away from the x-term first!

Q: How do I convert 13/2 to a mixed number?

Divide 13 by 2: 13 ÷ 2 = 6 remainder 1. So $ \frac{13}{2} = 6\frac{1}{2} $. The quotient becomes the whole number, remainder goes over the divisor.

Q: What if I get confused by the negative signs?

Write each step carefully! When you have $ -2x = -13 $, remember that negative ÷ negative = positive. Think: "What times -2 gives -13? A positive number!"

Q: Why is my answer different from the other choices?

Common wrong answers come from sign errors or arithmetic mistakes. Double-check your division: $ \frac{-13}{-2} = +6\frac{1}{2} $, not negative!

Linear Equations with Mixed Number Solutions

$13-2x=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this problem.

00:06 We need to focus on the letter X.

00:10 Rearrange the equation to get X by itself.

00:13 Keep working to isolate X completely.

00:19 And that's how we find our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$13-2x=0$

Step-by-step solution

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

Step 1: Subtract 13 from both sides of the equation to isolate the term with $x$ .
Step 2: Divide by $-2$ to solve for $x$ .

Now, let's work through each step:
Step 1: Begin by subtracting 13 from both sides:

$13 - 2x - 13 = 0 - 13$
Which simplifies to:

$-2x = -13$

Step 2: Divide both sides by $-2$ to solve for $x$ :

$\frac{-2x}{-2} = \frac{-13}{-2}$

This simplifies to:

$x = \frac{13}{2}$

When expressed as a mixed number, $x$ equals:

$x = 6\frac{1}{2}$ .

Therefore, the solution to the problem is $x = 6\frac{1}{2}$ .

The correct answer choice is :

$x = 6\frac{1}{2}$

Final Answer

$x=6\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Isolation: Move constants to one side before dividing by coefficient
Division: Divide -13 by -2 gives positive result: 13/2
Verification: Substitute back: 13 - 2(6½) = 13 - 13 = 0 ✓

Common Mistakes

Avoid these frequent errors

Forgetting negative signs when dividing
Don't divide -13 by -2 and get -6½ = wrong sign! Negative divided by negative gives positive. Always remember that (-) ÷ (-) = (+) when solving equations.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I subtract 13 from both sides first?

You need to isolate the term with x before dividing. If you divide first, you'd have messy fractions to work with. Always move constants away from the x-term first!

How do I convert 13/2 to a mixed number?

Divide 13 by 2: 13 ÷ 2 = 6 remainder 1. So $\frac{13}{2} = 6\frac{1}{2}$ . The quotient becomes the whole number, remainder goes over the divisor.

What if I get confused by the negative signs?

Write each step carefully! When you have $-2x = -13$ , remember that negative ÷ negative = positive. Think: "What times -2 gives -13? A positive number!"

Can I check my answer a different way?

Yes! Try graphing or thinking logically: if x = 6½, then 2x = 13, so 13 - 13 = 0. You can also use mental math to verify mixed number calculations.

Why is my answer different from the other choices?

Common wrong answers come from sign errors or arithmetic mistakes. Double-check your division: $\frac{-13}{-2} = +6\frac{1}{2}$ , not negative!

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