Which expression equals half a number x decreased by six?

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

Which expression equals half a number x decreased by six?

Explanation:
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.

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