The correct option :
[tex] =\tt (a) \: 4[/tex]
Steps to derive correct option :
[tex] = \frac{x + 1}{x + 3} = \frac{15}{21} [/tex]
[tex] =( x + 1 )\times 21 = (x + 3 )\times 15[/tex]
[tex] = 21x + 21 = 15x + 45[/tex]
[tex] = 21x + 21 - 15x = 45[/tex]
[tex] = 6x + 21 = 45[/tex]
[tex] = 6x = 45 - 21[/tex]
[tex] = 6x = 24[/tex]
[tex] = x = \frac{24}{6} [/tex]
[tex] =\color{plum} \bold{x = 4}[/tex]
Let us now place 4 in the place of x and see if the substitution is equivalent to [tex] \frac{15}{21} [/tex] :
[tex] = \frac{4 + 1}{4 + 3} = \frac{15}{21} [/tex]
[tex] = \frac{5}{7} = \frac{15}{21} [/tex]
[tex] = \frac{5}{7} = \frac{15÷3}{21÷3} [/tex]
[tex] = \frac{5}{7} = \frac{5}{7} [/tex]
Therefore, the value of x in this proportion = 4
