Solve for y: 3y - 7 > 2y + 5.

Solve for y: 3y - 7 > 2y + 5.

• A. y > 7
• B. y > 12
• C. y < 12
• D. y ≥ 12

Answer: (B)

Solving a linear inequality means isolating the variable while keeping the inequality sign in the appropriate direction. Start with 3y - 7 > 2y + 5. Subtract 2y from both sides to collect the y terms: y - 7 > 5. Then add 7 to both sides: y > 12. The direction of the inequality stays the same because we only added and subtracted the same amount on both sides. The boundary point where equality would occur is y = 12, so values strictly greater than 12 satisfy the inequality. You can check with y = 13: 3(13) - 7 = 32 and 2(13) + 5 = 31, and 32 > 31. A value of y = 12 gives 29 = 29, which does not satisfy the strict >. Therefore, the solution is y > 12.

Solving a linear inequality means isolating the variable while keeping the inequality sign in the appropriate direction. Start with 3y - 7 > 2y + 5. Subtract 2y from both sides to collect the y terms: y - 7 > 5. Then add 7 to both sides: y > 12. The direction of the inequality stays the same because we only added and subtracted the same amount on both sides. The boundary point where equality would occur is y = 12, so values strictly greater than 12 satisfy the inequality. You can check with y = 13: 3(13) - 7 = 32 and 2(13) + 5 = 31, and 32 > 31. A value of y = 12 gives 29 = 29, which does not satisfy the strict >. Therefore, the solution is y > 12.