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Difficulty: Very hardSolving One-Variable Linear Equations

What is the value of xx in the equation below?

3−25(10x−15)=12(4x+8)−7x3 - \frac{2}{5}(10x - 15) = \frac{1}{2}(4x + 8) - 7x
  1. A
    -13
  2. B
    7
  3. -5Answer
  4. D
    3

Answer

-5
The correct answer is -5. By distributing the fractional coefficients, combining like terms, and isolating the variable, the equation simplifies to -4x + 9 = -5x + 4, which yields x = -5.

Step-by-Step Solution

1
Distribute the fractional coefficients on both sides of the equation.
3−4x+6=2x+4−7x3 - 4x + 6 = 2x + 4 - 7x
To eliminate the parentheses and prepare the equation for combining like terms. Carefully manage the negative sign when distributing -2/5.
2
Combine the constant terms on the left side and the variable terms on the right side.
−4x+9=−5x+4-4x + 9 = -5x + 4
To simplify both sides of the equation before isolating the variable.
3
Add 5x to both sides of the equation.
x+9=4x + 9 = 4
To keep the equation balanced while moving all x terms to one side.
4
Subtract 9 from both sides of the equation.
x=−5x = -5
To isolate the variable x and find its final value.

Key Concept

Solving multi-step linear equations involving fractions, distribution, and variables on both sides.
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Topics

Solving One-Variable Linear Equations

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