Solving a Simple Equation: Find X in 3x - 5 = 4x + 11

Q: Why is my answer negative? Did I make a mistake?

Negative answers are completely normal! In this problem, x = -16 is correct. Always check your work by substituting back into the original equation rather than assuming negative means wrong.

Q: Should I move the x terms or the numbers first?

Either approach works! You can move x terms first (like subtracting 3x) or constants first (like adding 5). Choose whichever feels more comfortable, but be consistent with your signs.

Q: How do I remember which direction to move terms?

Think "opposite operation": if you see +11, subtract 11 from both sides. If you see -5, add 5 to both sides. The term disappears from one side and appears on the other.

Q: What if I get confused with the signs?

Write each step carefully and double-check your arithmetic. Remember: $ -5 - 11 = -16 $, not +6. When subtracting a positive number from a negative, you get more negative.

Linear Equations with Negative Solutions

Solve for X:

$3x-5=4x+11$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Let's arrange the equation so that one side has only the unknown X

00:24 Collect like terms

00:29 Convert from negative to positive

00:37 Negative divided by negative always equals positive

00:40 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:

$3x-5=4x+11$

Step-by-step solution

To solve this problem, we will follow a series of algebraic steps:

Step 1: Begin with the equation $3x - 5 = 4x + 11$ .
Step 2: Subtract $3x$ from both sides to start isolating the variable $x$ on one side:
$-5 = 4x - 3x + 11$ .
Step 3: Simplify the right side:
$-5 = x + 11$ .
Step 4: Subtract 11 from both sides to isolate $x$ :
$-5 - 11 = x$ .
Step 5: Simplify the left side:
$-16 = x$ .

Thus, the solution to the problem is $x = -16$ .

Final Answer

-16

Key Points to Remember

Essential concepts to master this topic

Rule: Move all x terms to one side and constants to the other
Technique: Subtract 3x from both sides: -5 = x + 11
Check: Substitute x = -16: 3(-16) - 5 = 4(-16) + 11 gives -53 = -53 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting when moving terms
Don't add 3x to both sides when you see 3x - 5 = 4x + 11 = wrong operations! This creates 6x - 5 = x + 11 and gives x = 16 instead of -16. Always subtract terms to move them to the opposite side.

Practice Quiz

Test your knowledge with interactive questions

Solve for $$ b $$ :

$$ 8-b=6 $$

FAQ

Everything you need to know about this question

Why is my answer negative? Did I make a mistake?

Negative answers are completely normal! In this problem, x = -16 is correct. Always check your work by substituting back into the original equation rather than assuming negative means wrong.

Should I move the x terms or the numbers first?

Either approach works! You can move x terms first (like subtracting 3x) or constants first (like adding 5). Choose whichever feels more comfortable, but be consistent with your signs.

How do I remember which direction to move terms?

Think "opposite operation": if you see +11, subtract 11 from both sides. If you see -5, add 5 to both sides. The term disappears from one side and appears on the other.

What if I get confused with the signs?

Write each step carefully and double-check your arithmetic. Remember: $-5 - 11 = -16$ , not +6. When subtracting a positive number from a negative, you get more negative.

Can I solve this equation differently?

Yes! You could start by adding 5 to both sides, then subtracting 4x. Multiple paths lead to the same answer: x = -16. Use the method that makes most sense to you.

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