Solve for X in the Linear Equation: 3-x=1

Q: Why do I get -x = -2 instead of x = 2 directly?

Because x has a negative coefficient in the original equation! When you isolate the x-term, you get -x on one side. You need one more step: multiply both sides by -1.

Q: Can I add x to both sides instead of subtracting 3?

Yes! Adding x to both sides gives you $ 3 = 1 + x $, then subtract 1: $ x = 2 $. Both methods work perfectly!

Q: How do I remember to multiply by -1 at the end?

Remember: you want positive x, not negative x. If you see -x = [number], you're not done yet. Multiply both sides by -1 to flip the signs.

Q: Why can't x equal 1 or 3?

Test them! If x = 1: $ 3 - 1 = 2 \neq 1 $. If x = 3: $ 3 - 3 = 0 \neq 1 $. Only x = 2 makes the equation true.

Linear Equations with Negative Variables

Solve for X:

$3-x=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Isolate the unknown X

00:18 Reduce what we can

00:34 Convert from negative to positive

00:40 Negative times negative is always equal to positive

00:47 And this is 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:

$3-x=1$

Step-by-step solution

To solve the equation $3 - x = 1$ , we will isolate the variable $x$ .

Step 1: Subtract 3 from both sides of the equation.
$3 - x - 3 = 1 - 3$
Step 2: Simplify the expression.
$-x = -2$
Step 3: Multiply both sides by $-1$ to solve for $x$ .
$x = 2$

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

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Isolate the variable by undoing operations in reverse order
Technique: Subtract 3 from both sides: 3-x-3 = 1-3 gives -x = -2
Check: Substitute x=2 back into original: 3-2 = 1 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to handle the negative sign correctly
Don't leave your answer as -x = -2 thinking x = -2! This ignores that x has a negative coefficient. Always multiply both sides by -1 to get x = 2.

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 get -x = -2 instead of x = 2 directly?

Because x has a negative coefficient in the original equation! When you isolate the x-term, you get -x on one side. You need one more step: multiply both sides by -1.

Can I add x to both sides instead of subtracting 3?

Yes! Adding x to both sides gives you $3 = 1 + x$ , then subtract 1: $x = 2$ . Both methods work perfectly!

What if I accidentally make the equation 3 + x = 1?

That's a different equation entirely! Always double-check that you're copying the original equation correctly before solving. Small sign errors lead to completely wrong answers.

How do I remember to multiply by -1 at the end?

Remember: you want positive x, not negative x. If you see -x = [number], you're not done yet. Multiply both sides by -1 to flip the signs.

Why can't x equal 1 or 3?

Test them! If x = 1: $3 - 1 = 2 \neq 1$ . If x = 3: $3 - 3 = 0 \neq 1$ . Only x = 2 makes the equation true.

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