QuestionChoose the expressions equivalent to $8(3 x+1)$ : $3 x+8$ , $(3 x+1) 8$ , $24 x+8$ , $8(1+3 x)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $8(3x+1)$ . . We need to find the expressions that are equivalent to this.

STEP 2

First, let's simplify the given expression by using the distributive property of multiplication over addition. This property states that for all real numbers a, b, and c, the equation $a(b + c) = ab + ac$ holds true.
So, we can write the given expression as8(x+1) =8 \cdotx +8 \cdot1

STEP 3

Now, let's simplify the expression further by performing the multiplication.
$8 \cdot3x +8 \cdot1 =24x +8$

STEP 4

Now, let's compare this simplified expression with the given options.
The first option is $3x +8$ , which is not equivalent to $24x +8$ .
The second option is $(3x +1)8$ . This is the same as the original expression, but with the factors reversed. The commutative property of multiplication states that for all real numbers a and b, the equation $ab = ba$ holds true. So, this option is equivalent to the original expression.
The third option is $24x +8$ , which is exactly the same as our simplified expression.
The fourth option is $8(1 +3x)$ . This is the same as the original expression, but with the terms inside the parentheses reversed. The commutative property of addition states that for all real numbers a and b, the equation $a + b = b + a$ holds true. So, this option is equivalent to the original expression.
So, the expressions equivalent to $8(3x+1)$ are $(3x+1)8$ , $24x+8$ , and $8(1+3x)$ .

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