Solve for x in the equation: 19(x + y) + 17 = 19(-x + y) – 21
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Answer: A. -1
Explanation
Expanding both sides of the linear equation removes the parentheses and prepares terms for combination. Isolating the variable terms on one side of the equation simplifies the algebraic expression significantly. Solving the resulting linear relationship yields an exact negative one value for the unknown variable. Linear equations contain variables raised only to the first power without any exponent terms. Distributing coefficients across parentheses is a fundamental algebraic rule for simplifying equations. Balancing equations requires performing identical mathematical operations on both sides simultaneously.
Algebraic equation solving is the cornerstone of advanced mathematics, physics, and financial modeling. Software developers use linear equations to determine unknown parameters in graphic rendering algorithms. Mastering basic equation manipulation builds confidence for tackling complex multi-variable calculus problems. Option B suggests a negative two value which fails to satisfy the balanced equation equality. Option C proposes a negative three value that creates an arithmetic imbalance across the equals sign. Option D introduces a negative four solution that violates the foundational linear expansion rules.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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