Solve for y: 2(y - 4) = 3y + 6

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Solve for y: 2(y - 4) = 3y + 6

Explanation:
Solving a linear equation with parentheses and variables on both sides uses distribution, then gathering like terms and isolating the variable. Distribute on the left: 2(y - 4) becomes 2y - 8, so the equation is 2y - 8 = 3y + 6. Move the y terms to one side by subtracting 2y from both sides, yielding -8 = y + 6. Isolate y by subtracting 6 from both sides, giving -14 = y, so y = -14. Check by substitution: replace y with -14. Left side: 2(-14 - 4) = 2(-18) = -36. Right side: 3(-14) + 6 = -42 + 6 = -36. Both sides match, so -14 is correct.

Solving a linear equation with parentheses and variables on both sides uses distribution, then gathering like terms and isolating the variable.

Distribute on the left: 2(y - 4) becomes 2y - 8, so the equation is 2y - 8 = 3y + 6. Move the y terms to one side by subtracting 2y from both sides, yielding -8 = y + 6. Isolate y by subtracting 6 from both sides, giving -14 = y, so y = -14.

Check by substitution: replace y with -14. Left side: 2(-14 - 4) = 2(-18) = -36. Right side: 3(-14) + 6 = -42 + 6 = -36. Both sides match, so -14 is correct.

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