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QuestionFind expressions equivalent to (−2z−1)+(−5z−3)(-2 z-1)+(-5 z-3).

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions that are equivalent to (−z−1)+(−5z−3)(- z-1)+(-5 z-3).

STEP 2

First, we simplify the given expression by combining like terms.(−2z−1)+(−5z−)=−2z−5z−1−(-2 z-1)+(-5 z-) = -2z -5z -1 -

STEP 3

Combine the zz terms and the constant terms.
−2z−5z−1−3=−7z−-2z -5z -1 -3 = -7z -

STEP 4

Now, we compare the simplified expression −7z−4-7z -4 with the given options.

STEP 5

implify the first option (−2z−1)+(−3z−5)(-2 z-1)+(-3 z-5).
(−2z−1)+(−3z−5)=−2z−3z−1−5=−5z−(-2 z-1)+(-3 z-5) = -2z -3z -1 -5 = -5z -This is not equivalent to −7z−4-7z -4.

STEP 6

implify the second option −2z+−5z−3−1-2 z+-5 z-3-1.
−2z+−5z−3−1=−2z−5z−3−1=−z−4-2 z+-5 z-3-1 = -2z -5z -3 -1 = -z -4This is equivalent to −z−4-z -4.

STEP 7

implify the third option (−z−2)+(−5z−3)(-z-2)+(-5 z-3).
(−z−2)+(−5z−3)=−z−5z−2−3=−6z−5(-z-2)+(-5 z-3) = -z -5z -2 -3 = -6z -5This is not equivalent to −7z−4-7z -4.

STEP 8

implify the fourth option −2z−4+−5z-2 z-4+-5 z.
−2z−4+−5z=−2z−5z−4=−7z−4-2 z-4+-5 z = -2z -5z -4 = -7z -4This is equivalent to −7z−4-7z -4.
The expressions equivalent to (−2z−1)+(−5z−3)(-2 z-1)+(-5 z-3) are −2z+−5z−3−1-2 z+-5 z-3-1 and −2z−4+−5z-2 z-4+-5 z.

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