Which expression equals half a number x decreased by six?

Which expression equals half a number x decreased by six?

• A. x/2 - 6
• B. (x-6)/2
• C. (6 - x)/2
• D. x/2 + 6

Answer: (A)

Translating the phrase into an algebraic expression. Half of a number x means multiply x by 1/2, giving x/2. Then “decreased by six” means subtract 6 from that result. So the expression is x/2 minus 6, written as x/2 - 6. For contrast, if you tried (x-6)/2, that would be half of (x minus 6), which equals x/2 - 3, not the same. If you used (6 - x)/2, you’d get half of (6 minus x), which is 3 - x/2, again not the same. And x/2 + 6 would be adding six, not decreasing by six. A quick check: if x = 10, half is 5, then minus six gives -1, and x/2 - 6 = 10/2 - 6 = 5 - 6 = -1, which matches.

Translating the phrase into an algebraic expression. Half of a number x means multiply x by 1/2, giving x/2. Then “decreased by six” means subtract 6 from that result. So the expression is x/2 minus 6, written as x/2 - 6.

For contrast, if you tried (x-6)/2, that would be half of (x minus 6), which equals x/2 - 3, not the same. If you used (6 - x)/2, you’d get half of (6 minus x), which is 3 - x/2, again not the same. And x/2 + 6 would be adding six, not decreasing by six.

A quick check: if x = 10, half is 5, then minus six gives -1, and x/2 - 6 = 10/2 - 6 = 5 - 6 = -1, which matches.