Given that y = -6x + 1 and -3 < x < $\frac{2}{3}$ . Then y lies in which of the following intervals.

(a) (18, -4)

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(b) (3, 19)

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(d) (-3,19)

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Solution

The correct option is D (d) (-3,19)
Given that,
-3 < x < $\frac{2}{3}$ .
Here we need to convert x into y using the properties of inequalities that we learnt. So we wil start with multiplying the given inequality with -6. Since this is a negative number the inequality sign reverses
-3 (-6) > x.(-6) > $\frac{2}{3}$ (-6).
18 > -6 x > -4

Now adding 1 to the inequality.
19 > -6 x + 1 > - 3

i.e., 19 > y > -3
y ∊ (-3, 19)

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