Math

QuestionChoose the equivalent expressions for 7(3p+2)8p7(-3 p+2)-8 p: - 11p+14-11 p+14 - 29p+14-29 p+14 - 3(7p+2)8p-3(7 p+2)-8 p - 7(4p+p+2)8p7(-4 p+p+2)-8 p

Studdy Solution

STEP 1

Assumptions1. We are given the expression 7(3p+)8p7(-3 p+)-8 p. . We need to find the expressions that are equivalent to the given expression.

STEP 2

First, we need to simplify the given expression. We can do this by distributing the7 through the parentheses and then combining like terms.
7(p+2)8p=21p+148p7(- p+2)-8 p = -21 p +14 -8 p

STEP 3

Combine like terms.
21p+148p=29p+14-21 p +14 -8 p = -29 p +14

STEP 4

Now, we need to compare the simplified expression with the given options.
The first option is 11p+14-11 p+14. This is not equivalent to our simplified expression, 29p+14-29 p +14.
The second option is 29p+14-29 p+14. This is equivalent to our simplified expression, 29p+14-29 p +14.
The third option is 3(7p+2)8p-3(7 p+2)-8 p. We need to simplify this expression to compare it with our simplified expression.

STEP 5

implify the third option.
3(7p+2)8p=21p8p=29p-3(7 p+2)-8 p = -21 p - -8 p = -29 p -This is not equivalent to our simplified expression, 29p+14-29 p +14.
The fourth option is 7(4p+p+2)8p7(-4 p+p+2)-8 p. We need to simplify this expression to compare it with our simplified expression.

STEP 6

implify the fourth option.
(4p+p+2)8p=(3p+2)8p=21p+148p=29p+14(-4 p+p+2)-8 p =(-3 p +2) -8 p = -21 p +14 -8 p = -29 p +14This is equivalent to our simplified expression, 29p+14-29 p +14.
The expressions equivalent to (3p+2)8p(-3 p+2)-8 p are 29p+14-29 p+14 and (4p+p+2)8p(-4 p+p+2)-8 p.

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