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Solve the equation. Check your solution.−3(4y+2)−12=−8(y+4)+4y-3(4y+2)-12=-8(y+4)+4y

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Solve the equation. Check your solution.−3(4y+2)−12=−8(y+4)+4y-3(4y+2)-12=-8(y+4)+4y
  1. Distribute −3-3: Distribute the −3-3 into the parentheses on the left side of the equation.\newline−3×4y=−12y-3 \times 4y = -12y\newline−3×2=−6-3 \times 2 = -6\newlineSo, the left side of the equation becomes −12y−6-12y - 6.
  2. Distribute −8-8: Distribute the −8-8 into the parentheses on the right side of the equation.\newline−8×y=−8y-8 \times y = -8y\newline−8×4=−32-8 \times 4 = -32\newlineSo, the right side of the equation becomes −8y−32-8y - 32.
  3. Combine terms: Add the 4y4y term on the right side of the equation to the −8y-8y term.\newline−8y+4y=−4y-8y + 4y = -4y\newlineNow, the right side of the equation is −4y−32-4y - 32.
  4. Write simplified equation: Write down the simplified equation from the previous steps.\newline−12y−6−12=−4y−32-12y - 6 - 12 = -4y - 32
  5. Combine like terms: Combine like terms on the left side of the equation. \newline−12y−6−12-12y - 6 - 12 becomes −12y−18-12y - 18.
  6. Isolate y term: Now we have the equation −12y−18=−4y−32-12y - 18 = -4y - 32. Add 12y12y to both sides to get all the y terms on one side. −12y+12y−18=−4y+12y−32-12y + 12y - 18 = -4y + 12y - 32 This simplifies to −18=8y−32-18 = 8y - 32.
  7. Add 3232: Add 3232 to both sides to isolate the yy term.\newline−18+32=8y−32+32-18 + 32 = 8y - 32 + 32\newlineThis simplifies to 14=8y14 = 8y.
  8. Divide by 88: Divide both sides by 88 to solve for yy.148=8y8\frac{14}{8} = \frac{8y}{8}This simplifies to y=148y = \frac{14}{8}, which can be further simplified to y=74y = \frac{7}{4}.

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