QuestionChoose the equivalent expressions for $(-7 b-3)-(2 b+3)$ .

Studdy Solution

STEP 1

Assumptions1. We are given four expressions and we need to find the expressions that are equivalent to $(-7 b-3)-( b+3)$ . . The operations involved are subtraction and multiplication.
3. The order of operations (BIDMAS/BODMAS) will be followed.

STEP 2

First, let's simplify the given expression $(-7 b-)-(2 b+)$ .
According to the distributive property of multiplication over addition, we can distribute the negative sign to each term inside the parentheses.
$(-7 b-)-(2 b+) = -7 b - -2 b -$

STEP 3

Now, combine like terms.
$-7 b -3 -2 b -3 = -9 b -6$

STEP 4

Now, let's compare the simplified expression $-9 b -6$ with the given expressions.
The first expression is $(-3 b-7)-(3 b+2)$ . Simplifying this, we get $(-3 b-7)-(3 b+2) = -3 b -7 -3 b -2 = -6 b -9$

STEP 5

The second expression is $(-7 b-3)-(3 b+2)$ . Simplifying this, we get $(-7 b-3)-(3 b+2) = -7 b -3 -3 b -2 = -10 b -5$

STEP 6

The third expression is $- b+-2 b-6$ . Simplifying this, we get $- b+-2 b-6 = -9 b -6$

STEP 7

The fourth expression is $-15 b$ . This is already simplified and does not match with our simplified expression $-9 b -6$ .

STEP 8

Now, comparing the simplified expressions, we see that the only expression equivalent to $(-7 b-3)-(2 b+3)$ is $-7 b+-2 b-6$ .
So, the expressions equivalent to $(-7 b-3)-(2 b+3)$ are $-7 b+-2 b-6$ .

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