Final answer:
Solve the presented linear equation by simplifying each side, combining like terms, and then isolating 'y' to find that y = -2. Verify the solution by substituting it back into the original equation.
Step-by-step explanation:
The student has presented a linear equation to solve and check: 4-[4+5y-3(y+5)]=-3(2y-5)-[8(y-1)-10y+12]. To solve this equation, we need to simplify and solve for 'y'.
First, simplify both sides of the equation:
On the left: 4 - (4 + 5y - 3y - 15)
On the right: -3(2y - 5) - (8y - 8 - 10y + 12)
Simplify further:
On the left: 4 - 4 - 5y + 3y + 15
On the right: -6y + 15 - 8y + 8 + 10y - 12
Combine like terms:
On the left: 5y - 3y = 2y, and 4 - 4 + 15 = 15
On the left becomes: 15 - 2y
On the right: -6y - 8y + 10y = -4y, and 15 + 8 - 12 = 11
On the right becomes: -4y + 11
Now we have the simpler equation: 15 - 2y = -4y + 11. Add 2y to both sides to get all the y terms on one side and all constant terms on the other side.
Add 2y to both sides: 15 = -2y + 11
Then, subtract 11 from both sides: 4 = -2y
Finally, divide both sides by -2 to solve for y:
y = -2
To check, substitute y=-2 back into the original equation and see if both sides are equal.