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Difficulty: MediumSolving One-Variable Linear Equations

An algebraic equation requires simplification to isolate the unknown variable. Which of the following represents the correct value of yy in the equation below?

3(2y+5)−y=2(2y−1)+13 3(2y + 5) - y = 2(2y - 1) + 13
  1. A
    0
  2. B
    6
  3. -4Answer
  4. D
    26

Answer

The correct value for yy is −4-4.
The correct answer is found by properly applying the distributive property to both sides, combining the resulting like terms, and systematically isolating the variable. Maintaining the balance of the equation by performing inverse operations yields a final value of -4.

Step-by-Step Solution

1
Distribute the constants into the parentheses on both sides of the equation.
6y+15−y=4y−2+136y + 15 - y = 4y - 2 + 13
To eliminate the parentheses and prepare the equation for combining terms.
2
Combine like terms on each individual side.
5y+15=4y+115y + 15 = 4y + 11
To simplify the expressions on both sides before isolating the variable.
3
Subtract 4y4y from both sides.
y+15=11y + 15 = 11
To group all variable terms onto the left side of the equation.
4
Subtract 1515 from both sides.
y=−4y = -4
To completely isolate yy and find the final root of the equation.

Key Concept

Solving one-variable linear equations by applying the distributive property and combining like terms.
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Topics

Solving One-Variable Linear Equations

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