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Difficulty: MediumSolving One-Variable Linear Equations

Consider the following mathematical relationship:

34(m−8)+2=12m−1 \frac{3}{4}(m - 8) + 2 = \frac{1}{2}m - 1

Which of the following represents the correct solution for mm?

  1. 12Answer
  2. B
    14
  3. C
    -20
  4. D
    21

Answer

The correct solution is 12.
The correct solution is found by systematically applying the distributive property to eliminate parentheses, combining the constant terms, grouping the variable terms on one side, and fully isolating the variable. Following these steps accurately yields a value of 12.

Step-by-Step Solution

1
Apply the distributive property to the left side of the equation.
34m−6+2=12m−1 \frac{3}{4}m - 6 + 2 = \frac{1}{2}m - 1
This removes the parentheses by multiplying the fraction through the terms inside.
2
Combine the constant terms on the left side.
34m−4=12m−1 \frac{3}{4}m - 4 = \frac{1}{2}m - 1
Simplifying the expressions on both sides makes it easier to isolate the variable.
3
Subtract 12m \frac{1}{2}m from both sides to group the variable terms.
14m−4=−1 \frac{1}{4}m - 4 = -1
This places all terms containing the variable on one side of the equation. (Note: 34m−24m=14m \frac{3}{4}m - \frac{2}{4}m = \frac{1}{4}m )
4
Add 4 to both sides to isolate the variable term.
14m=3 \frac{1}{4}m = 3
This cancels out the constant on the left side, leaving only the variable term.
5
Multiply both sides by 4.
m=12 m = 12
This clears the fractional coefficient and solves for the final value of the variable.

Key Concept

Solving one-variable linear equations with fractions and distribution
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Topics

Solving One-Variable Linear Equations

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