Solve Linear Equation: 5b+2b-7+14=0 for Variable b

Linear Equations with Like Term Combining

5b+2b7+14=0 5b+2b-7+14=0

b=? b=?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Group factors
00:10 Let's isolate variable B
00:28 This is the solution to the question

Step-by-step written solution

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1

Understand the problem

5b+2b7+14=0 5b+2b-7+14=0

b=? b=?

2

Step-by-step solution

It's important to remember that when we have regular numbers and unknowns, we cannot add or subtract them directly.

Let's collect like terms:

5b+2b-7+14=0

7b+7 = 0

Let's move terms

7b = -7

Let's divide by 7

b=-1

And that's the solution!

3

Final Answer

1 -1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Combine like terms before solving the equation
  • Technique: Group variable terms: 5b + 2b = 7b
  • Check: Substitute back: 5(-1) + 2(-1) - 7 + 14 = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Adding variables and constants together
    Don't combine 5b - 7 = -2b! Variables and constants are different types and cannot be combined. This creates completely wrong equations. Always combine only like terms: variables with variables (5b + 2b) and constants with constants (-7 + 14).

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

What are like terms exactly?

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Like terms have the same variable part. In this problem, 5b and 2b are like terms (both have 'b'), while -7 and 14 are like terms (both are just numbers).

Why can't I combine 5b and -7?

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Because 5b represents 5 times some unknown number, while -7 is just -7. You can't add apples and oranges! Only combine terms that have the exact same variable part.

What if I get the signs wrong when combining?

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Be extra careful with signs! For 5b + 2b, both are positive so you get 7b. For -7 + 14, you're adding a negative and positive, so think: 14 - 7 = 7.

Do I always move terms to one side?

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Yes! After combining like terms, isolate the variable by moving all terms without the variable to the opposite side. This gives you the cleanest path to the solution.

How do I know which side to move terms to?

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It doesn't matter! You can move the constant to the right (7b = -7) or the variable to the left (-7 = -7b). Choose whichever feels easier - both give the same answer.

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