Solve the Linear Equation: Finding X in 3 = 5 - X

Q: Why do I add x to both sides when the equation has -x?

When you have -x in an equation, adding positive x to both sides cancels out the negative x. Think of it as: -x + x = 0, which eliminates the x from that side!

Q: Can I subtract 5 from both sides first instead?

Yes, but it's usually easier to move the variable first. If you subtract 5 first, you get -2 = -x, then you need to divide by -1 or multiply by -1 to get x = 2.

Q: What if I get a negative answer?

Negative answers are perfectly valid! Always check your work by substituting back into the original equation to make sure both sides are equal.

Q: How do I know which operation to use first?

Look for the simplest way to isolate x. In $ 3 = 5 - x $, adding x to both sides gets rid of the subtraction, making it easier to solve.

Q: Why does 3 + x = 5 give us x = 2?

We have 3 + x = 5Subtract 3 from both sides: x = 5 - 3Simplify: x = 2The goal is always to get x by itself!

Linear Equations with Variable Isolation

Solve for X:

$3=5-x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the value of X.

00:07 We'll rearrange the equation so X is on one side.

00:16 Next, gather like terms together.

00:22 Change negatives to positives.

00:30 Remember: a negative divided by a negative is positive.

00:35 And that gives us the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$3=5-x$

Step-by-step solution

To solve the equation $3 = 5 - x$ , we need to isolate $x$ . We'll perform a sequence of simple algebraic manipulations:

Step 1: Add $x$ to both sides of the equation to move $x$ to the left side. This gives us:

$3 + x = 5$

Step 2: Subtract 3 from both sides of the equation to solve for $x$ :

$x = 5 - 3$

Step 3: Simplify the right side:

$x = 2$

Therefore, the solution to the equation is $x = 2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Use inverse operations to isolate the variable on one side
Technique: Add x to both sides first: 3 + x = 5
Check: Substitute back: 3 = 5 - 2 becomes 3 = 3 ✓

Common Mistakes

Avoid these frequent errors

Subtracting x from both sides instead of adding
Don't subtract x from both sides when you have -x = you'll get 3 - x = 5 - x - x which becomes 3 - x = 5 - 2x! This makes the equation more complex. Always add x to both sides to eliminate the negative coefficient.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I add x to both sides when the equation has -x?

When you have -x in an equation, adding positive x to both sides cancels out the negative x. Think of it as: -x + x = 0, which eliminates the x from that side!

Can I subtract 5 from both sides first instead?

Yes, but it's usually easier to move the variable first. If you subtract 5 first, you get -2 = -x, then you need to divide by -1 or multiply by -1 to get x = 2.

What if I get a negative answer?

Negative answers are perfectly valid! Always check your work by substituting back into the original equation to make sure both sides are equal.

How do I know which operation to use first?

Look for the simplest way to isolate x. In $3 = 5 - x$ , adding x to both sides gets rid of the subtraction, making it easier to solve.

Why does 3 + x = 5 give us x = 2?

We have 3 + x = 5
Subtract 3 from both sides: x = 5 - 3
Simplify: x = 2

The goal is always to get x by itself!

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