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Sagot :
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
[tex]\begin{gathered} 4(x+3)+2x \\ x=3 \\ 4(3+3)+2(3)=4\times6+6=24+6=30 \\ 6(x+2) \\ x=3 \\ 6(3+2)=6\times5=30 \end{gathered}[/tex]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
[tex]\begin{gathered} x=5 \\ a\text{. 4(x+3) + 2x} \\ 4(5+3)+2(5)=4\times8+10=32+10=42 \\ b\text{. 6(x+2)} \\ 6(5+2)=30+12=42 \end{gathered}[/tex]option b is also equivalent
let's test for option c
x = 1
[tex]\begin{gathered} x=1 \\ 4(x+3)+2x \\ 4(1+3)+2(1)=4\times4+2=18 \\ 6(x+2)=6(1+2)=6\times3=18 \end{gathered}[/tex]option c is also equivalent
x = 8
[tex]\begin{gathered} x=8 \\ 4(x+3)+2x \\ 4(8+3)+2(8) \\ 4\times11+16=44+16=60 \\ 6(x+2) \\ 6(8+2)=6\times10=60 \end{gathered}[/tex]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
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