Question

1. solve the compound inequality.

$2(x - 2) + 7 > -1$ and $5 - 4x > 9$
a $x < -2$ and $x < 1$
b $x > -2$ and $x < 1$
c $x < -2$ and $x < -1$
d $x > -2$ and $x < -1$

Explanation:

Step1: Simplify first inequality

Expand and isolate $x$:
$$2(x-2)+7 > -1$$
$$2x - 4 + 7 > -1$$
$$2x + 3 > -1$$
$$2x > -4$$
$$x > -2$$

Step2: Simplify second inequality

Isolate $x$ (reverse inequality when dividing by negative):
$$5 - 4x > 9$$
$$-4x > 4$$
$$x < -1$$

Answer:

D. $x > -2$ and $x < -1$