Question 11

x equals 60

To solve the equation 3x - 12 = 2x + 48, we find that x equals 60 after isolating the variable on one side of the equation.

A) 60

This option is correct because when substituting x with 60 in the original equation, both sides yield the same result: 3(60) - 12 equals 180, and 2(60) + 48 also equals 180, confirming that x = 60 satisfies the equation.

B) 36

Option B is incorrect. If we substitute x with 36, we find that the left side becomes 3(36) - 12, which equals 96, and the right side becomes 2(36) + 48, which equals 120. Since 96 does not equal 120, x = 36 does not satisfy the equation.

C) -12

This option is also incorrect. Substituting x with -12 results in the left side being 3(-12) - 12, which equals -48, while the right side, 2(-12) + 48, equals 24. Since -48 does not equal 24, x = -12 does not satisfy the equation.

D) 12

Option D is not correct either. If we substitute x with 12, the left side calculates to 3(12) - 12, which equals 24, and the right side calculates to 2(12) + 48, which equals 72. Therefore, since 24 does not equal 72, x = 12 does not satisfy the equation.

Conclusion

Option A is definitively correct because it accurately satisfies the original equation, while all other options fail to do so. The process of solving the equation clearly demonstrates that only x = 60 balances both sides, confirming its validity.