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Difficulty: MediumSolving One-Variable Linear Equations
Calculate the exact value of nn that balances the following equation:
23(6n−9)+4=3(n−2)−n \frac{2}{3}(6n - 9) + 4 = 3(n - 2) - n

Answer: -2

Answer

The correct value for n is -2.
The solution is found by correctly applying the distributive property to both sides of the equation, combining like terms to simplify the expression to 4n−2=2n−64n - 2 = 2n - 6, and then isolating the variable nn using inverse operations to get n=−2n = -2.

Step-by-Step Solution

1
Distribute the fraction on the left side of the equation.
4n - 6 + 4 = 3(n - 2) - n
To eliminate the parentheses on the left side and isolate the individual terms.
2
Distribute the coefficient on the right side of the equation.
4n - 6 + 4 = 3n - 6 - n
To expand the expressions before combining them.
3
Combine like terms on both sides.
4n - 2 = 2n - 6
To simplify the equation into the standard linear form ax + b = cx + d.
4
Group the variable terms on one side and the constants on the other.
2n = -4
By subtracting 2n and adding 2 to both sides, we isolate the variable term.
5
Divide by the coefficient of n.
n = -2
To solve for the isolated variable n.

Key Concept

Solving multi-step linear equations involving fractions, distribution, and combining like terms.
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Topics

Solving One-Variable Linear Equations

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