PROBLEM
Find expressions equivalent to −2(h−5): −2(h−5), (h−5)⋅−2, −2h+10.
STEP 1
Assumptions1. We are looking for expressions that are equivalent to −(h−5). The expressions given are (h−5)⋅−, (−+h)⋅−5, (−5+h)⋅−, and −h+10
STEP 2
First, we need to simplify the given expression −2(h−5).
−2(h−5)=−2⋅h+2⋅5
STEP 3
Calculate the simplified expression.
−2(h−5)=−2⋅h+2⋅5=−2h+10
STEP 4
Now, let's compare this simplified expression with the given expressions. The first expression is (h−)⋅−2.
(h−)⋅−2=−2⋅h+2⋅
STEP 5
Calculate the simplified expression.
(h−5)⋅−2=−2⋅h+2⋅5=−2h+10
STEP 6
The simplified expression for (h−5)⋅−2 is equivalent to the simplified expression for −2(h−5), so (h−5)⋅−2 is equivalent to −2(h−5).
STEP 7
The second expression is (−2+h)⋅−5.
(−2+h)⋅−5=−5⋅−2+−5⋅h
STEP 8
Calculate the simplified expression.
(−2+h)⋅−5=−5⋅−2+−5⋅h=10−5h
STEP 9
The simplified expression for (−2+h)⋅−5 is not equivalent to the simplified expression for −2(h−5), so (−2+h)⋅−5 is not equivalent to −2(h−5).
STEP 10
The third expression is (−5+h)⋅−2.
(−5+h)⋅−2=−2⋅−5+−2⋅h
STEP 11
Calculate the simplified expression.
(−5+h)⋅−=−⋅−5+−⋅h=10−h
STEP 12
The simplified expression for (−5+h)⋅−2 is not equivalent to the simplified expression for −2(h−5), so (−5+h)⋅−2 is not equivalent to −2(h−5).
STEP 13
The fourth expression is −2h+10.
−2h+10=−2h+10
SOLUTION
The expression −2h+10 is equivalent to the simplified expression for −2(h−), so −2h+10 is equivalent to −2(h−).
The expressions equivalent to −2(h−) are (h−)⋅−2 and −2h+10.
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