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

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

• A. -14
• B. -15
• C. -13
• D. -12

Answer: (A)

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.