If 5 + x, 2x + 7, 6x + 9, and y are in proportion when x = 2, find the value of y.

Four terms 5 + x, 2x + 7, 6x + 9, and y are in proportion.

Value of x = 2.

If four terms a, b, c, and d are in proportion, then:

​$$\frac{a}{b} = \frac{c}{d}$$​​

which implies $$a \cdot d = b \cdot c$$​​

Terms are in proportion, so;

​$$\frac{5+x}{2x + 7} = \frac{6x + 9}{y}$$​​

Putting x = 2 ,

​$$\frac{5+2}{2 \times 2+7} = \frac{6 \times 2+9}{y}$$​​

​$$\frac{7}{11} = \frac{21}{y}$$​​

​$$\implies y = \frac{ 21 \times 11}{7}= 33$$​​

Thus, the value of y is 33.