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Zorluk: OrtaSolving One-Variable Linear Equations

Which of the following values for mm makes the equation true?

35(10m−15)−4m=12(8m+14)−34 \frac{3}{5}(10m - 15) - 4m = \frac{1}{2}(8m + 14) - 34
  1. A
    6
  2. 9Cevap
  3. C
    18
  4. D
    3

Cevap

The correct answer is 9.
The correct answer is found by properly executing the distributive property on both sides to clear the parentheses. On the left side, 3/5 is distributed to yield 6m - 9. On the right side, 1/2 is distributed to yield 4m + 7. After combining the remaining like terms, the equation simplifies to 2m - 9 = 4m - 27. Adding 27 and subtracting 2m from both sides gives 18 = 2m, which simplifies to m = 9.

Adım Adım Çözüm

1
Distribute the fractions into the parentheses on both sides of the equation.
6m−9−4m=4m+7−346m - 9 - 4m = 4m + 7 - 34
The distributive property must be applied first to expand the expressions and eliminate the parentheses.
2
Combine like terms on each side of the equal sign.
2m−9=4m−272m - 9 = 4m - 27
Simplifying each side individually makes it easier to isolate the variable in subsequent steps.
3
Subtract 2m from both sides.
−9=2m−27-9 = 2m - 27
This gathers all variable terms on one side of the equation.
4
Add 27 to both sides and divide the result by 2.
18=2m18 = 2m, which means m=9m = 9
This isolates the variable completely and provides the final solution.

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Solving One-Variable Linear Equations
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Solving One-Variable Linear Equations

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