Question

Svetlana's hair is 3 cm long. Her hair

grows 1.5 cm per month. Svetlana wanter
her hair to be less than 18 cm long. Write
an inequality to determine the number of
months Svetlana can allow her hair to
grow. Then, solve the inequality.

Answer 1

Required inequality is 1.5x + 3 < 18 and solution is x < 10, that is number of months svetlana can allow her hair to grow must be less than 10 so that her hair length will be less that 18 cm

Solution:

Given that

Svetlana's hair is 3 cm long.

Her hair grows 1.5 cm per month

Need to write an inequality to determine the number of months Svetlana can allow her hair to grow.

Let assume number of months Svetlana can allow her hair to grow be represented by variable "x"

Length of hair grows in one month = 1.5 cm

So Length of hair grows in "x" months =
`\text { Length of hair grows in one month } * x=1.5 * x=1.5 x`

As Svetlana wanted her hair to be less than 18 cm long

So Length of hair grows in "x" months plus current length of hair must be less than 18 cm

=> 1.5x + 3 < 18

On solving the above inequality for "x" we get ,

1.5x < 18 – 3

=> 1.5x < 15

=>
`x < (15)/(1.5)`

=> x < 10

Thus required inequality is 1.5x + 3 < 18

Number of months sultana can allow her hair to grow must be less than 10 so that her hair length will be less that 18 cm.