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Question

Difficulty: MediumSolving One-Variable Linear Equations

What is the exact numerical value of the variable pp that balances the given algebraic equation?

Answer:−2(3p−5)+4p=3(p+5)−20-2(3p - 5) + 4p = 3(p + 5) - 20

Value: 【3】

Answer

3
The correct answer is found by first distributing the outer values into the parentheses, taking special care to distribute the negative sign accurately so that −2(−5)=10-2(-5) = 10. After expanding, the equation becomes −6p+10+4p=3p+15−20-6p + 10 + 4p = 3p + 15 - 20. Combining the like terms on each side reduces the equation to −2p+10=3p−5-2p + 10 = 3p - 5. Adding 2p2p to both sides and adding 55 to both sides isolates the terms, resulting in 15=5p15 = 5p. Finally, dividing both sides by 5 yields a value of 3.

Step-by-Step Solution

1
Distribute the constants into the parentheses on both sides of the equation.
−6p+10+4p=3p+15−20-6p + 10 + 4p = 3p + 15 - 20
Expanding the grouped terms is necessary to access and combine all the variable and constant terms.
2
Combine the like terms on each side of the equation separately.
−2p+10=3p−5-2p + 10 = 3p - 5
Simplifying each side independently reduces the complexity before moving variables across the equals sign.
3
Isolate the variable by moving all pp terms to one side and all constants to the opposite side.
10+5=3p+2p10 + 5 = 3p + 2p, which simplifies to 15=5p15 = 5p
Adding 2p2p and adding 55 to both sides gathers the unknown variable exclusively to the right and constants to the left.
4
Divide by the coefficient of the variable to solve for pp.
p=3p = 3
Dividing both sides by 5 leaves the variable pp completely isolated, providing the final solution.

Key Concept

Applying the distributive property and balancing operations to solve multi-step linear equations.
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Topics

Solving One-Variable Linear Equations

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