Solve for y: 4y - 9 = 3y + 7.

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Multiple Choice

Solve for y: 4y - 9 = 3y + 7.

Explanation:
Solving a linear equation means getting the variable by itself on one side while keeping the equation balanced. Here you want to collect the y terms on one side. Subtract 3y from both sides to move the y term over: 4y - 9 - 3y = 3y + 7 - 3y, which simplifies to y - 9 = 7. Then add 9 to both sides to isolate y: y - 9 + 9 = 7 + 9, giving y = 16. To verify, substitute y = 16: 4(16) - 9 = 64 - 9 = 55, and 3(16) + 7 = 48 + 7 = 55, so both sides match. Other values don’t balance the equation (for example, y = 7 gives 19 on the left and 28 on the right; y = -2 gives -17 versus 1; y = 3 gives 3 versus 16), so the solution is y = 16.

Solving a linear equation means getting the variable by itself on one side while keeping the equation balanced. Here you want to collect the y terms on one side. Subtract 3y from both sides to move the y term over: 4y - 9 - 3y = 3y + 7 - 3y, which simplifies to y - 9 = 7. Then add 9 to both sides to isolate y: y - 9 + 9 = 7 + 9, giving y = 16.

To verify, substitute y = 16: 4(16) - 9 = 64 - 9 = 55, and 3(16) + 7 = 48 + 7 = 55, so both sides match.

Other values don’t balance the equation (for example, y = 7 gives 19 on the left and 28 on the right; y = -2 gives -17 versus 1; y = 3 gives 3 versus 16), so the solution is y = 16.

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