Question

Which best proves why the expressions 4(x+3)+2x and 6(x+2) must be equivalent expressions?B When x= 3, both expressions have a value of 30.When x-5, both expressions have a value of 42.• When x-1both expressions have a value of 18, and when X-8, both expressions have a value of 60.When x - 2, both expressions have a value of 15, and when x-6, both expressions have a value of 39.Type here to search

Answer 1

hello

the question here asks if the given expressions are equivalent?

for an expression to be equivalent, the must have the same value when a particular variable is substituted into them

for example 2(x + 1) and x + 5 are equivalent variables when x = 2

now with the question presented here

4(x + 3) + 2x and 6(x + 2)

the first option said that when x = 3, the expression value = 30

let's test this

`\begin{gathered} 4(x+3)+2x \\ x=3 \\ 4(3+3)+2(3)=4*6+6=24+6=30 \\ 6(x+2) \\ x=3 \\ 6(3+2)=6*5=30 \end{gathered}`

from the calculations, the expressions are equivalent when x = 3 the resultant vale equals 30

option A is equivalent

let's test for the second one

when x = 5, the value of the expression equals 42

`\begin{gathered} x=5 \\ a\text{. 4(x+3) + 2x} \\ 4(5+3)+2(5)=4*8+10=32+10=42 \\ b\text{. 6(x+2)} \\ 6(5+2)=30+12=42 \end{gathered}`

option b is also equivalent

let's test for option c

x = 1

`\begin{gathered} x=1 \\ 4(x+3)+2x \\ 4(1+3)+2(1)=4*4+2=18 \\ 6(x+2)=6(1+2)=6*3=18 \end{gathered}`

option c is also equivalent

x = 8

`\begin{gathered} x=8 \\ 4(x+3)+2x \\ 4(8+3)+2(8) \\ 4*11+16=44+16=60 \\ 6(x+2) \\ 6(8+2)=6*10=60 \end{gathered}`

option D is also equivalent

from the options given, they are all equivalent although any of the options could prove the reason why they're equivalent, x = 1 proves it best because it easier to solve