Solve Linear Equation: 3x+4+8x-15=0 Step by Step

Linear Equations with Like Terms

3x+4+8x15=0 3x+4+8x-15=0

x=? x=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Collect terms
00:14 Positive times negative always equals negative
00:21 Isolate the unknown X
00:36 Simplify what we can
00:42 Isolate the unknown X
00:53 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3x+4+8x15=0 3x+4+8x-15=0

x=? x=\text{?}

2

Step-by-step solution

To solve the equation 3x+4+8x15=0 3x + 4 + 8x - 15 = 0 , we begin by combining the terms that involve x x and the constant terms:

Step 1: Combine like terms.
The terms involving x x are 3x 3x and 8x 8x . Adding these yields:

11x 11x

The constant terms are +4 +4 and 15-15. Combining these gives:

+415=11 +4 - 15 = -11

Thus, the equation becomes:

11x11=0 11x - 11 = 0

Step 2: Solve for x x .
To isolate x x , add 11 to both sides of the equation:

11x11+11=0+11 11x - 11 + 11 = 0 + 11 11x=11 11x = 11

Now, divide both sides by 11:

x=1111 x = \frac{11}{11} x=1 x = 1

Therefore, the solution to the equation is x=1 x = 1 .

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always combine like terms before solving for the variable
  • Technique: Combine 3x+8x=11x 3x + 8x = 11x and 415=11 4 - 15 = -11
  • Check: Substitute x=1 x = 1 : 3(1)+4+8(1)15=0 3(1) + 4 + 8(1) - 15 = 0

Common Mistakes

Avoid these frequent errors
  • Solving before combining like terms
    Don't try to solve 3x=4 3x = -4 and 8x=15 8x = 15 separately = two different wrong answers! This creates confusion and incorrect solutions. Always combine 3x+8x=11x 3x + 8x = 11x and 415=11 4 - 15 = -11 first, then solve 11x11=0 11x - 11 = 0 .

Practice Quiz

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\( \frac{-y}{5}=-25 \)

FAQ

Everything you need to know about this question

What are like terms exactly?

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Like terms have the same variable raised to the same power. In this problem, 3x 3x and 8x 8x are like terms because both have x to the first power. Constants like 4 and -15 are also like terms.

Why can't I solve for x right away?

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You need to simplify first to see the equation clearly! With multiple x terms scattered around, you might miss some or make calculation errors. Combining like terms gives you one clean equation to solve.

What if I get the signs wrong when combining?

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Be extra careful with positive and negative signs! Remember that +415=11 +4 - 15 = -11 , not +11. Write each step clearly: 4+(15)=11 4 + (-15) = -11 .

How do I know I combined everything correctly?

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Count your terms! The original equation has 4 terms, and after combining you should have 2 terms: one x-term and one constant. If you still have more than 2 terms, keep combining!

Is there a faster way to solve this?

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Not really - combining like terms is the fastest way! Trying shortcuts usually leads to mistakes. This systematic approach works for any linear equation, no matter how complex.

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