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QuestionChoose the equivalent expressions for (−2z−1)+(−5z−(−2z−1))(-2 z-1)+(-5 z-(-2 z-1)).

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions that are equivalent to (−z−1)+(−5z−3)(- z-1)+(-5 z-3). Two expressions are equivalent if they simplify to the same result

STEP 2

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

STEP 3

Now, we combine the terms to simplify the expression.
−2z−5z−1−3=−7z−-2z -5z -1 -3 = -7z -

STEP 4

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

STEP 5

First, we simplify the expression (−2z−1)+(−3z−5)(-2 z-1)+(-3 z-5).
(−2z−1)+(−3z−5)=−2z−3z−1−5(-2 z-1)+(-3 z-5) = -2z -3z -1 -5

STEP 6

Now, we combine the terms to simplify the expression.
−2z−3z−1−5=−5z−6-2z -3z -1 -5 = -5z -6

STEP 7

The expression −5z−6-5z -6 is not equivalent to −7z−4-7z -4.

STEP 8

Next, we simplify the expression −2z+−5z−3−1-2 z+-5 z-3-1.
−2z+−5z−3−1=−2z−5z−3−1-2 z+-5 z-3-1 = -2z -5z -3 -1

STEP 9

Now, we combine the terms to simplify the expression.
−2z−5z−3−=−7z−4-2z -5z -3 - = -7z -4

STEP 10

The expression −7z−4-7z -4 is equivalent to −7z−4-7z -4.

STEP 11

Next, we simplify the expression (−z−)+(−5z−3)(-z-)+(-5 z-3).
(−z−)+(−5z−3)=−z−5z−−3(-z-)+(-5 z-3) = -z -5z - -3

STEP 12

Now, we combine the terms to simplify the expression.
−z−5z−2−=−6z−5-z -5z -2 - = -6z -5

STEP 13

The expression −6z−5-6z -5 is not equivalent to −7z−-7z -.

STEP 14

Finally, we simplify the expression −2z−4+−z-2 z-4+- z.
−2z−4+−z=−2z−z−4-2 z-4+- z = -2z -z -4

STEP 15

Now, we combine the terms to simplify the expression.
−2z−5z−4=−7z−4-2z -5z -4 = -7z -4

STEP 16

The expression −z−4-z -4 is equivalent to −z−4-z -4.
So, the expressions that are equivalent to (−2z−)+(−5z−3)(-2 z-)+(-5 z-3) are −2z+−5z−3−-2 z+-5 z-3- and −2z−4+−5z-2 z-4+-5 z.

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