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Question

Difficulty: MediumSolving One-Variable Linear Equations

Which of the following represents the value of yy that makes the given equation true?

2y−53+8=3\frac{2y - 5}{3} + 8 = 3
  1. -5Answer
  2. B
    0
  3. C
    5
  4. D
    19

Answer

The correct value for the variable is -5.
The solution requires a sequence of inverse operations to isolate the variable. First, subtracting 8 from both sides gives a value of -5 on the right. Then, multiplying by 3 clears the fraction, resulting in 2y - 5 = -15. Adding 5 yields 2y = -10, and dividing by 2 confirms the final value is -5.

Step-by-Step Solution

1
Isolate the fractional term by subtracting 8 from both sides of the equation.
2y−53=−5\frac{2y - 5}{3} = -5
Applying the inverse operation of addition moves the constant term to the right side, simplifying the equation.
2
Multiply both sides of the equation by 3.
2y−5=−152y - 5 = -15
Multiplying by the denominator eliminates the fraction, making it possible to solve for the variable.
3
Add 5 to both sides of the equation.
2y=−102y = -10
This step isolates the term with the variable on the left side.
4
Divide both sides by 2.
y=−5y = -5
Dividing by the coefficient of the variable gives the final exact value.

Key Concept

Solving one-variable linear equations involving fractions
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Topics

Solving One-Variable Linear Equations

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