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Solve the equation. Check your solution.
-3(4y+2)-12=-8(y+4)+4y
The solution set is _____. Type an integer or a simplified fraction.

Solve the equation. Check your solution.\newline3(4y+2)12=8(y+4)+4y-3(4 y+2)-12=-8(y+4)+4 y\newlineThe solution set is _____\_\_\_\_\_. Type an integer or a simplified fraction.

Full solution

Q. Solve the equation. Check your solution.\newline3(4y+2)12=8(y+4)+4y-3(4 y+2)-12=-8(y+4)+4 y\newlineThe solution set is _____\_\_\_\_\_. Type an integer or a simplified fraction.
  1. Distribute 3-3: Distribute the 3-3 into the parentheses on the left side of the equation.\newlineCalculation: \(-3(44y) + 3-3(22) - 1212 = 12-12y - 66 - 1212
  2. Combine like terms: Combine like terms on the left side of the equation.\newlineCalculation: 12y612=12y18-12y - 6 - 12 = -12y - 18
  3. Distribute 8-8: Distribute the 8-8 into the parentheses on the right side of the equation.\newlineCalculation: \(-8(y) + 8-8(44) + 44y = 8-8y - 3232 + 44y
  4. Combine like terms: Combine like terms on the right side of the equation.\newlineCalculation: 8y32+4y=4y32-8y - 32 + 4y = -4y - 32
  5. Set equal: Set the simplified left side equal to the simplified right side.\newlineCalculation: 12y18=4y32-12y - 18 = -4y - 32
  6. Add 4y4y: Add 4y4y to both sides to get all the y terms on one side.\newlineCalculation: 12y+4y18=4y+4y32-12y + 4y - 18 = -4y + 4y - 32\newlineSimplification: 8y18=32-8y - 18 = -32
  7. Add 1818: Add 1818 to both sides to isolate the yy term.\newlineCalculation: 8y18+18=32+18-8y - 18 + 18 = -32 + 18\newlineSimplification: 8y=14-8y = -14
  8. Divide by 8-8: Divide both sides by 8-8 to solve for yy.\newlineCalculation: 8y/8=14/8-8y / -8 = -14 / -8\newlineSimplification: y=14/8y = 14/8
  9. Simplify fraction: Simplify the fraction to get the final answer.\newlineCalculation: y=148=74y = \frac{14}{8} = \frac{7}{4}

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