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Difficulty: MediumSolving One-Variable Linear Equations

Solve the following equation for the variable nn:

2n−43=n+52\frac{2n - 4}{3} = \frac{n + 5}{2}

What is the correct value of nn?

  1. A
    1
  2. B
    7
  3. C
    9
  4. 23Answer

Answer

The correct value for the variable is 23.
The correct value is 23, which is found by properly cross-multiplying the fractions, distributing the values to all terms in the numerators, and maintaining equality while isolating the variable.

Step-by-Step Solution

1
Cross-multiply to eliminate the fractions.
2(2n−4)=3(n+5)2(2n - 4) = 3(n + 5)
Multiplying each side's numerator by the other side's denominator clears the fractions from the equation.
2
Distribute the constants on both sides of the equation.
4n−8=3n+154n - 8 = 3n + 15
Applying the distributive property removes the parentheses so like terms can be combined.
3
Subtract 3n3n from both sides.
n−8=15n - 8 = 15
This moves all variable terms to the left side of the equation to begin isolating nn.
4
Add 8 to both sides.
n=23n = 23
This isolates the variable nn to find the final solution.

Key Concept

Solving One-Variable Linear Equations
Estimated Time:1m 30s
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Topics

Solving One-Variable Linear Equations

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