Question

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

• A. $\left(18,-4\right)$
• B. $\left(3,19\right)$
• C. $\left(-19,3\right)$
• D. $\left(-3,19\right)$

Answer 1

The correct option is D $\left(-3,19\right)$

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
$-3\left(-6\right)>x\cdot \left(-6\right)>\frac{2}{3}\cdot \left(-6\right)$
$18>-6x>-4$

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

i.e., $19>y>-3$
$y\in \left(-3,19\right)$