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We begin by simplifying the given equation:
First, we combine like terms on the left side of the equation:
This simplifies to:
Now the equation is:
Next, we need to isolate by moving the constant term to the right side. We do this by subtracting 56 from both sides:
Simplifying the right-hand side gives us:
Finally, to solve for , we divide both sides by 43:
This simplifies to:
Therefore, the solution to the problem is .
1
\( x+7=14 \)
\( x=\text{?} \)
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.
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.
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.
Yes! You could subtract 56 from both sides first to get . However, it's usually easier to combine like terms first to simplify the equation before moving constants.
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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