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

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Prepare for the 8th Grade FAST Mathematics Test with our Pre-Algebra quiz. Study with multiple choice questions, each with hints and explanations. Build your confidence and ensure you're ready to excel!

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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