Solve Linear Equation: 37b + 6b + 56 = 90 + 9

Linear Equations with Like Terms

37b+6b+56=90+9 37b+6b+56=90+9

b=? b=\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
00:09 We want to isolate the unknown B
00:14 Let's arrange the equation so that B is only on one side
00:26 Isolate the unknown B
00:34 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

37b+6b+56=90+9 37b+6b+56=90+9

b=? b=\text{?}

2

Step-by-step solution

We begin by simplifying the given equation:

37b+6b+56=90+9 37b + 6b + 56 = 90 + 9

First, we combine like terms on the left side of the equation:

(37+6)b+56 (37 + 6)b + 56

This simplifies to:

43b+56 43b + 56

Now the equation is:

43b+56=99 43b + 56 = 99

Next, we need to isolate b b by moving the constant term to the right side. We do this by subtracting 56 from both sides:

43b=9956 43b = 99 - 56

Simplifying the right-hand side gives us:

43b=43 43b = 43

Finally, to solve for b b , we divide both sides by 43:

b=4343 b = \frac{43}{43}

This simplifies to:

b=1 b = 1

Therefore, the solution to the problem is b=1 b = 1 .

3

Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Combine Like Terms: Add coefficients of same variables: 37b + 6b = 43b
  • Isolate Variable: Move constants to one side: subtract 56 from both sides
  • Verification: Substitute b = 1 back: 43(1) + 56 = 99 ✓

Common Mistakes

Avoid these frequent errors
  • Combining unlike terms incorrectly
    Don't add variable terms to constant terms like 37b + 56 = 93b! This mixes different types of terms and gives wrong results. Always combine only like terms: variables with variables (37b + 6b = 43b) and constants with constants (90 + 9 = 99).

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 and how do I identify them?

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Like terms have the same variable with the same power. In this problem, 37b and 6b are like terms because they both have the variable b. Constants like 56, 90, and 9 are also like terms with each other.

Why do I combine like terms first before moving constants?

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Combining like terms simplifies the equation and makes it easier to solve. It's like organizing your work - gather all the b terms together, then deal with moving the numbers around.

What if I get a different answer when I check?

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If substituting your answer doesn't work, go back and check each step. Common errors include: wrong arithmetic when combining terms, sign errors when moving terms, or division mistakes.

Can I move the 56 to the right side first instead?

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Yes! You could subtract 56 from both sides first to get 43b=43 43b = 43 . However, it's usually easier to combine like terms first to simplify the equation before moving constants.

How do I know when to add or subtract the constant?

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Look at the sign in front of the constant. Since we have +56 with the variable term, we subtract 56 from both sides to cancel it out. Always do the opposite operation to move terms.

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