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Difficulty: HardSolving One-Variable Linear Equations

Consider the linear equation provided below:

−2(y−8)+3y=4(y−1)−y+10 -2(y - 8) + 3y = 4(y - 1) - y + 10

Which of the following numbers correctly satisfies this equation?

  1. A
    11
  2. 5Answer
  3. C
    0
  4. D
    -11

Answer

The correct value that satisfies the equation is 5.
The correct answer is found by first distributing the values outside the parentheses, maintaining the positive sign when multiplying -2 by -8. This results in -2y + 16 + 3y = 4y - 4 - y + 10. Combining like terms simplifies the equation to y + 16 = 3y + 6. Finally, isolating the variable by subtracting y and 6 from both sides gives 10 = 2y, which divides cleanly to 5.

Step-by-Step Solution

1
Distribute the outside coefficients into their respective parentheses.
−2y+16+3y=4y−4−y+10 -2y + 16 + 3y = 4y - 4 - y + 10
Distribution eliminates the parentheses, ensuring careful attention to multiplying the negative coefficient (−2×−8=+16-2 \times -8 = +16).
2
Combine the like variable terms and constant terms on each side independently.
y+16=3y+6 y + 16 = 3y + 6
Simplifying each side makes it easier to track and isolate the variable in the next steps.
3
Isolate the variable terms on one side by subtracting yy from both sides.
16=2y+6 16 = 2y + 6
Gathering all variable terms on a single side is required to solve for the unknown.
4
Isolate the constant terms by subtracting 6 from both sides, then divide by 2.
10=2y⇒y=5 10 = 2y \Rightarrow y = 5
Using inverse operations isolates yy to reveal its final numerical value.

Key Concept

Solving One-Variable Linear Equations
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Topics

Solving One-Variable Linear Equations

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