2([tex]\frac{2}{5}[/tex]x + 4) = [tex]\frac{4}{5}[/tex]x + 4 which is the second option is the equivalent expression.
Explanation:
First, we need to calculate the value of two-fifths of x. It means 2 portions out of the five portions of x which equates to [tex]\frac{2}{5}[/tex]x.
Now we calculate the values of the two expresssions on the LHS.
1) 2 (two-fifths x + 2) = 2 ([tex]\frac{2}{5}[/tex]x + 2) = [tex]\frac{4}{5}[/tex]x + 4.
2) (two-fifths x + 4) = 2([tex]\frac{2}{5}[/tex]x + 4) = [tex]\frac{4}{5}[/tex]x + 8.
Now we determine values of the four expressions on the RHS.
1) Two and two-fifths x + 1 = 2[tex]\frac{2}{5}[/tex]x + 1
2) Four-fifths x + 4 = [tex]\frac{4}{5}[/tex]x + 4
3) Four-fifths x + 2 = [tex]\frac{4}{5}[/tex]x + 2
4) Two and two-fifths x + 8 = 2[tex]\frac{2}{5}[/tex]x + 8.
Out of the various LHS and RHS values, the [tex]1^{st}[/tex] LHS value and [tex]2^{nd}[/tex] RHS value is the same. So option 2 is the answer.
