Math

QuestionFind expressions equivalent to (4d1)+(7d6)(-4 d-1)+(-7 d-6).

Studdy Solution

STEP 1

Assumptions1. We are looking for expressions that are equivalent to (4d1)+(7d6)(-4 d-1)+(-7 d-6). The expressions must be simplified to their simplest form to check for equivalence

STEP 2

First, let's simplify the given expression (4d1)+(7d6)(-4 d-1)+(-7 d-6) by combining like terms.
(4d1)+(7d6)=4d7d1+6(-4 d-1)+(-7 d-6) = -4d -7d -1 +6

STEP 3

Now, simplify the expression by combining the terms.
d7d1+6=11d+5-d -7d -1 +6 = -11d +5

STEP 4

Now, let's check the first expression 7d11-7 d-11 to see if it is equivalent to 11d+-11d +.
Since 7d11-7 d-11 is not the same as 11d+-11d +, it is not equivalent.

STEP 5

Next, let's check the second expression (d4)+(d7)(-d-4)+(- d-7).
First, simplify the expression by combining like terms.
(d4)+(d7)=dd4+7(-d-4)+(- d-7) = -d -d -4 +7

STEP 6

Now, simplify the expression by combining the terms.
d6d4+=d+3-d -6d -4 + = -d +3Since d+3-d +3 is not the same as 11d+5-11d +5, the second expression is not equivalent.

STEP 7

Next, let's check the third expression (7d+6)+(4d+1)(-7 d+-6)+(-4 d+-1).
First, simplify the expression by combining like terms.
(7d+6)+(4d+1)=7d4d61(-7 d+-6)+(-4 d+-1) = -7d -4d -6 -1

STEP 8

Now, simplify the expression by combining the terms.
7d4d61=11d7-7d -4d -6 -1 = -11d -7Since 11d7-11d -7 is not the same as 11d+5-11d +5, the third expression is not equivalent.

STEP 9

Finally, let's check the fourth expression 18d-18 d.
Since 18d-18 d is not the same as 11d+5-11d +5, the fourth expression is not equivalent.
Therefore, none of the given expressions are equivalent to (4d)+(7d6)(-4 d-)+(-7 d-6).

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